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Wittgenstein once wrote, “The philosopher strives to ﬁnd the liberating word, that is, the word that ﬁnally permits us to grasp what up until now has intangibly weighed down our consciousness.” Would Wittgenstein have been willing to describe the Tractatus as an attempt to ﬁnd “the liberating word”? The basic contention of this strikingly innovative new study of the Tractatus is that this is precisely the case. Matthew Ostrow argues that, far from seeking to offer a new theory in logic in the tradition of Frege and Russell, Wittgenstein from the very beginning viewed all such endeavors as the ensnarement of thought. Providing a lucid and systematic analysis of the Tractatus, Professor Ostrow argues that Wittgenstein’s ultimate aim is to put an end to philosophy itself. The book belongs to a new school of interpretation that sees the early Wittgenstein as denying the possibility of a philosophical theory as such. It is unique, however, in two respects. First, it is the only “nonstandard” reading that offers an extended account of the central topics of the Tractatus – the picture theory, the notion of the variable, ethics, the different sense of analysis, and the general form of the proposition. Second, it highlights the intrinsic obstacles to any kind of general or summary understanding of Wittgenstein’s thought. “ . . . an original, detailed and highly compelling interpretation of Wittgenstein’s philosophical aims and central concerns. Ostrow shares Diamond’s and Conant’s sense of dissatisfaction with the traditional readings of the work, but the interpretation he offers is signiﬁcantly different from theirs and represents the ﬁrst book-length attempt to develop an alternative approach in a systematic way which engages fully the details of Wittgenstein’s text.” – Marie McGinn, University of York

In order to view Wittgenstein as placing such primacy on the question of philosophy. the issue is almost entirely absent. While I continue to believe that such a connection exists and that it can be interestingly drawn. the original study. I believe that for Wittgenstein – early. does not understand the question of philosophy’s nature to be some “meta-issue. middle. at bottom. particularly those in the middle of the Philosophical Investigations. and late – the question of philosophy’s nature is the central question of all of philosophy. as it stood. Indeed. Such a contention may seem surprising. Nonetheless. I have come to the (perhaps painfully obvious) realization that a serious attempt to come to terms just with Wittgenstein’s Tractatus is more than enough for one book. we shall take as our starting point the complete set of remarks that make up the Tractatus.” but. rather. Such an approach makes it evident that Wittgenstein. as we shall read him. Instead of seeking to privilege the meager store of Wittgenstein’s general reﬂections on philosophy. For while Wittgenstein’s reﬂections on the philosophical activity. an attempt to draw a philosophical connection between the early Wittgenstein and Plato. Moreover.PREFACE
This book grew out of a larger project. in the Tractatus.116). But this will not be our approach. it might then seem that we would have to give extraordinary weight to just a few passages. we must acknowledge that these represent only a very small portion of his total writings. over time. forming the subject matter of a mere eight remarks (TLP 4. continues to draw me to Wittgenstein: the concern with the nature of philosophy itself.1 are among his most oft-quoted claims. was too ambitious. the text with which we shall chieﬂy be concerned here.111–4. what initially motivated the project is what. one that
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Preface pervades what one ordinarily would think of as the content of the discipline. The traditional concerns of philosophy are, we might say, transformed by Wittgenstein into the means by which we can reﬂect on philosophy. It is the fundamental task of what follows to seek to bring out how this can be the case. Many people have helped me, in one way or another, with the lengthy process of writing this book. First and foremost, I would like to thank the late Burton Dreben. I am thankful to him as a teacher: He showed me what it is to think about philosophy at the highest level. I am thankful to him as the keenest of critics and collaborators: He spent many hours with me working through the nuances of my reading of the Tractatus. And I am thankful to him as a friend: His kindness, humor, and interest in my work were invaluable to me. Nearly every page of this study reﬂects his powerful inﬂuence and I remain deeply indebted to him. Charles Griswold also played a central role in the birth and development of this book. His subtle and imaginative reading of the Platonic dialogues provided part of the spark for the initial project. Furthermore, I am deeply grateful to him for his ongoing support, advice, and encouragement. Juliet Floyd was exceedingly generous with her help and encouragement in nearly every phase of the writing process. Moreover, I have been very much inﬂuenced by her penetrating and original reading of Wittgenstein, and by exposure to the elegance of her philosophical style. I owe her a large debt of gratitude. I would also like to thank Terence Moore and Matthew Lord of Cambridge University Press and my Production Editor, Laura Lawrie, for their assistance and support. I am grateful as well to the Earhart Foundation for the two years of ﬁnancial support during the study that formed the indispensable background to this book. Many others have contributed to this study – perhaps at times without even realizing it – and indeed deserve greater acknowledgment than I can offer here. I have had extensive and very fruitful conversations about the Tractatus with Rosalind Carey, Denis McManus, Joe McDonald, Andrew Lugg, and Anat Biletzki, and about philosophy more generally with Bruce Fraser, Thomas Woodard, Lawrence Pasternack, Phil Cafaro, Klaus Brinkmann, David Roochnik, and my brothers, Michael and Daniel Ostrow. Victor Kestenbaum took an interest in my work and offered his advice and encouragement at
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Preface a time when these were sorely needed. David Stern provided very helpful comments on an earlier draft. I have also had enumerable philosophical conversations with my wife, Theresa Reed. For that alone she would deserve my ample thanks, but, happily, her involvement with this study has extended far beyond that capacity, far beyond, in truth, what I can begin to express. Sufﬁce it to say that this book would in no way have been possible without her. Finally, I would like to thank my father, Seymour Ostrow, and my late mother, Judith Alling, who I dearly wish were still here to discuss it with me.

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INTRODUCTION

I

Wittgenstein, in conversation with Moritz Schlick, once characterized his fundamental goal in philosophy as follows: “Everything we do consists in trying to ﬁnd the liberating word (erloesende Wort)” (VC 77). Similarly, we ﬁnd in The Big Typescript: “The philosopher strives to ﬁnd the liberating word, that is, the word that ﬁnally permits us to grasp what up until now has intangibly weighed down our consciousness” (PO 165).1 Both remarks were made in the 1930s, years after the publication of the Tractatus: with their depiction of philosophy as the pathway out of psychic encumbrance, they quite naturally call to mind Wittgenstein’s later, explicitly “therapeutic” thought (cf., e.g., PI 133). But, we might ask, could such claims be applied to Wittgenstein’s early work as well? Would Wittgenstein have been willing to describe the Tractatus itself as an effort to ﬁnd “the liberating word”? My fundamental contention in this book is that this is indeed the case, that, far from seeking to offer a new theory of logic, to continue the philosophical legacies of Frege and Russell, Wittgenstein from the start views all such endeavors as the ensnarement of thought. The Tractatus, I shall aim to show, is nothing but an attempt to set down in deﬁnitive fashion the way of release. For those involved in writing and reﬂecting on early analytic philosophy, such an assertion is likely at once to locate this study in the grid of a familiar set of dichotomies. It would seem to herald a nonmetaphysical interpretation of the Tractatus as opposed to a standard, metaphysical reading, an emphasis on the continuity of Wittgenstein’s thought rather than the notion of a radical break from an earlier,
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those expectations will be met by what follows. Russell. that the terms in which these standard oppositions are formulated are simply not adequate to the Tractatus. an insistence on the nonsensicality of the text’s propositions as against the possibility that they might manage to communicate a kind of indirect truth. we must realize that this is not just the language of Frege. They are. One might then imagine that what will here be proposed is an alternative vocabulary in terms of which our interpretation is to be conducted – our own set of privileged categories. Instead. what we must acknowledge at the start is just the problem that is posed by the attempt to interpret the Tractatus. that the philosophical commitments that are revealed in our own manner of textual analysis are the very subject matter of the Tractatus. to call into question the traditional language of philosophy.” “nonsense. The Tractatus seeks to expose the extraordinary confusions inherent in the process of philosophical inquiry. they lie at the heart of the Tractatus. on the contrary. is that we cannot insulate ourselves from the difﬁculties with which Wittgenstein is concerned. we might say. in one way or another. I would suggest that.Introduction more traditional philosophical stance. too much part of the problem to constitute a potential solution. But I shall argue shortly against any such strategy. that Wittgenstein leaves us completely unequipped for such questions. clinical distance as commentators on the text. I believe inevitably. et al. Moore. in a very broad sense. in one form or another.” and so forth ill-suited to any sort of explanatory task in this context.. But just this fact renders notions like “metaphysical. What we ﬁnd. we must be willing to allow that these might be our confusions as well. of course. If we grant that Wittgenstein’s aim here is. But what animates this book is the belief that that “sense” is entirely too broad – that is. as it were.2 And.
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. but also our language: precisely the depth and comprehensiveness of this text’s critique of philosophy deprives us of our. Do we really know in general just what it means for a proposition or set of propositions to be “metaphysical” rather than “nonmetaphysical”? Is the fundamental aim of a philosopher’s thought so open to view that we can at once recognize when a given piece of writing does or does not cohere with it? Do we understand the claim that a work of philosophy is simply “nonsense”? It is not. To understand and write about that text.

3 Nonetheless. on them. if not its details. it would appear difﬁcult to treat its author as someone who has intended to present a straightforward theory. when he has climbed out through them. a series of straightforward philosophical accounts: accounts of the proposition (the “picture theory”). as being patently false or absurd.” If we take this remark seriously. in opposition to the tradition. 5. let us then return to the remark with which we began.51) in the way that so many philosophers in the Western tradition have dismissed their predecessors’ claims – namely. beginning with Ramsey’s review4 and the responses of the Vienna positivists.9 Characteristic of this approach – which would include a quite diverse set of interpretations – is the insistence on treating the Wittgensteinian attack as if it presented. Perhaps
3
. the responses on the part of Tractarian commentators to this move have been varied. after all. Still. Such a view has in fact been implicit in much of the literature on the Tractatus. One rather large obstacle to this approach to the Tractatus is represented by remark 6. What does it really mean to read the Tractatus in terms of a fundamental concern to “liberate” us from philosophical confusion? One might well grant something of this sort as the young Wittgenstein’s aim. already in the Preface portray his book as intending to show that “the problems of philosophy” rest on “the misunderstanding of the logic of our language” (TLP.5351. These accounts are then criticized or modiﬁed by commentators in accordance with the demands that are presumably to be satisﬁed by a well-constructed philosophical theory. he does. over them. e. as an attempt to provide a refutation of the misunderstandings and errors of the past.7 Hacker. p.8 and Pears. and continuing with the work of more contemporary commentators like Black. the ineffability of logical form.Introduction
II
In order to get a preliminary view of the difﬁculties that we must confront. TLP 4.6 Hintikka.003.. Wittgenstein proclaims various philosophical positions to be “nonsense” (see. Here Wittgenstein famously declares: “My propositions are elucidatory in this way: he who understands me ﬁnally recognizes them as nonsensical (unsinnig). in traditional philosophical terms.54. the tautologous nature of logical truth. On this reading. and so forth.5 Stenius. one could quite naturally construe the basic form of the Tractarian critique. 6. a series of claims to be evaluated in terms of their truth value. 27).g.

Wittgenstein seems to suggest that. that value lies outside of the world. One notable example of the latter strategy is Carnap’s interpretation of the statements of the Tractatus as purely linguistic proposals.” something intelligible is nonetheless thereby expressed.1211 (“Thus a proposition ‘fa’ shows that in its sense the object a occurs. In these remarks and elsewhere. purely formal assertions that serve to clarify the logical syntax of the language of science.14 Hintikka. they are not like many traditional metaphysical assertions in being entirely nonsensical.13 Geach. In this sense. not things.”) and 4.”). that a common logical form binds together language and the world. To be sure. according to the standards of signiﬁcance established by the Tractatus. We are then led to suppose that Wittgenstein’s propositions – if not the propositions of all metaphysics – are nonsense only in a special sense. while the attempt to state what is properly to be shown results in what he calls “nonsense.115 (“[Philosophy] will mean the unspeakable by clearly displaying the speakable. they somehow manage to convey to us important philosophical truths: at the end of the book we “know” that. only it cannot be said. while philosophical propositions of the sort espoused by Wittgenstein (and the Vienna positivists) make no claims about the world and thus are not true or false.15 and Hacker.”). of course. the world is composed of facts.62 (“In fact. Instead. For such readers. silently to ourselves.16 The strategy they employ is motivated by remarks such as TLP 5. we cannot actually say these things. what solipsism means is quite correct.12 A second example of an explicit attempt at moderating the Tractatus’ view of its own utterances is found in commentators like Anscombe. this remark is regarded as striking. but not as a central feature to be accommodated within a satisfactory interpretation. so such commentators continue. or to ignore its consequences with respect to our understanding of the seemingly substantive details of the text. two propositions ‘fa’ and ‘ga’ that they are both about the same object. in reality. legitimate philosophy is to be understood as consisting of elucidations. they are not strictly utterable. but shows itself. but must only think them.10 A second type of response involves an attempt at softening the impact of the text’s harsh self-assessment. 4. Except. Still.Introduction most commonly the tendency has been to disregard this remark. they can be seen as having the empty character that Wittgenstein ascribes to the tautologous propositions of logic. and so on.11 For Carnap. or perhaps we may repeat them –
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its own statements really are nonsense. “unsaturated”. Frege. indirectly. I want then to consider it in some detail (my focus will be on Diamond’s initial paper). no deep features of reality that are somehow made manifest in Wittgenstein’s utterances. To begin with. we can’t say and we can’t whistle it either. and the elaboration of it provided by James Conant. as Diamond reads him. one he believes will not
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. refusing to countenance the possibility of any sort of meaningful gesture toward the ineffable.17 Diamond.54 and realize that. the object. For Frege.” dismisses as incoherent Benno Kerry’s contention that there can be concepts – like the concept “horse” – which also can function as objects. There is no Tractarian counterpart to the Kantian Ding an sich. Given the importance of the Conant/Diamond interpretation in framing the contemporary debate about the Tractatus. Diamond suggests that Wittgenstein’s conception of nonsense and his concomitant show/say distinction have their roots in Frege’s so-called concept “horse” problem. in the end. all the pronouncements of his text are just so much gibberish. in the article “Concept and Object. in effect. beginning with her important paper “Throwing Away the Ladder. Now I have a good deal of sympathy with – and have been much inﬂuenced by – Diamond’s approach. attributes to Wittgenstein the position of Ramsey in his oft-quoted criticism of the Tractatus’ notion of showing: “But what we can’t say. I think one must take care to be as clear as possible about what this position really comes to. as far as the Tractatus is concerned. as is indicated by the appearance there of the deﬁnite article.” has presented a central challenge to this reading – and. The peculiarity of having to maintain that the concept “horse” is not a concept is dismissed by Frege as an “awkwardness of language” (CP 185) and. Cora Diamond. Nonetheless. serves necessarily to ﬁll the gap left by the concept. but always with the acknowledgment that in so doing we have transgressed the strictly proper bounds of sense. she bites the bullet on Wittgenstein’s behalf and proclaims that. as a logical subject. then – “the concept ‘horse’ is a concept easily attained” – the ﬁrst three words do not designate a Fregean concept. In Kerry’s example. but. More recently. to the related interpretation offered by Carnap. a Fregean object.Introduction grudgingly – to another. as it can easily serve to mislead. plain and simple. as he also puts it. the concept/object distinction is mutually exclusive: a concept by its very nature is predicative or. conversely.”18 That is. moreover. we must take Wittgenstein at his word at 6. Instead.

1. Here we begin to see how Diamond draws the connection with Wittgenstein. For her.” A quite natural ﬁrst response to this approach focuses on the extraordinary expressive power it attributes to the supposed gibberish of the Tractatus. (Why haven’t any books been written claiming to have established the nonsensicality of the Carroll poem?) Wittgen6
. any more than it is obvious that the traditional claims of metaphysics have such a character. for her. For clearly it is not at once obvious that this text’s propositions are utter nonsense.” Toward that end. and so forth were plainly indistinguishable from Lewis Carroll’s “Jabberwocky. not things.”21 To attempt to ascribe any further content to Wittgenstein’s claims is. as transitional. Wittgenstein is fundamentally concerned to extend to the whole philosophical vocabulary Frege’s way of excluding notions like “function” and “concept.522 of the Tractatus. Diamond then terms remarks like the one expressing the difference between concepts and objects “transitional”. All these claims.Introduction be encountered in a logically perfect notation like his Begriffsschrift. 1. Instead. these remarks are recognized as completely without sense and are in fact inexpressible.” any more than we would suppose this about an attempt to state something about functions and objects from within the Begriffsschrift. is now seen as it really is – that is. Instead. Aristotle’s Metaphysics. like every other remark of the Tractatus. he is understood as having formulated a number of transitional statements – namely remarks 1–6. as a claim completely on par with “Socrates is frabble”20 or “ ’Twas brillig. statements about concepts and objects of the sort represented by Kerry’s example – indeed. But once we have effected this transition. in the Begriffsschrift. If it were obvious.19 their purpose is solely to lead us into the Begriffsschrift. if the Tractatus. Russell’s Principles of Mathematics. we cannot suppose ourselves to be left hinting at some important truth with a statement like “The world is the totality of facts. After we have read – and understood – the text.” none of these works could ever have the power to mislead. Thus. that there is such a division will come out in the distinctive use of the signs of the notation. the very claim that there is a fundamental distinction between concepts (or functions) and objects – will not be formulatable. to begin operating within its parameters. to “chicken out. will then have to be given up by the close of the Tractatus. and the slithy toves did gyre and gimble in the wabe.

suggesting. however. in short. Indeed.”24 The latter expression. if we did not already know that syntax and were not therefore at once inclined to call the expression “meaningless. we can still attempt to understand a person who would wish to proclaim such empty strings. the Tractatus is then seen as an attempt to. for Diamond.Introduction stein’s claims are then assumed to be capable of themselves effecting the “transition” Diamond describes.” but rather that he who understands me so recognizes them. as it were. the less easy it becomes to explain the possibility of our ever coming to recognize them as such. this remark does not proclaim that he who understands my propositions “ﬁnally recognizes them as nonsensical. conjure up the state of mind of someone who has an inclination toward metaphysics. For.”27 On this reading. is that the more that Witttgenstein’s claims are assimilated to ordinary nonsense sentences. their dissimilarity to pseudosentences like “Socrates is frabble.”25 Central to this part of her account is Wittgenstein’s emphasis in 6. as devoid of sense. are incapable of being understood in themselves. For while the Tractatus’ remarks. but this is a result of our understanding the syntax of the English language.”22 Diamond sketches in some detail Wittgenstein’s account of the precise way in which philosophical nonsense is to be viewed.23 But this is as much as to acknowledge the special character of the Tractarian propositions. It does this. always with a therapeutic intent – that is. after all. she points out. This involves “a kind of imaginative activity. one which she elaborates in a more recent article. Diamond. and the Method of Wittgenstein’s Tractatus. Imagination. an exercise of the capacity to enter into the taking of nonsense for sense.26 This distinction between understanding the utterer of nonsense and understanding the nonsense itself is. would seem to have none of the capacity for self-illumination that is thought to belong to the remarks of the Tractatus. however. of somehow bringing us to recognize the fact that they are. crucial. absolutely devoid of sense. We might say that it “shows us” that it does not make sense. with the aim of helping the individual explode the illusion that
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. might seem to have developed a response to this sort of objection. in particular. “Ethics. in “What Nonsense Might Be. The point.54 on himself as subject.” it surely could not itself teach us that (let alone why) this is the case. that he rejects (what Diamond takes to be) Carnap’s view that it consists of category errors. of the capacity to share imaginatively the inclination to think that one is thinking something in it. contrary to all appearances.

One wonders how imagination could bring us to “understand” a person. Diamond in this way believes she can account for the illuminating potential of the Tractarian remarks.28 what allows Wittgenstein’s nonsensical utterances to be liberating is just their utterer’s recognition of them as nonsense. alternatively. locating this not in those remarks’ “internal features.” but rather in external features of their use. In other words. but should not be viewed as saying anything more than that. especially “Throwing Away the Ladder” and its central idea of the Tractatus as a series of “transitional remarks.” That question can be brought into full view by here asking ourselves: transitional to what? I certainly agree with Cora Diamond’s premise that much of the original motivation for both the show/say distinction and the idea of “throwing away the ladder” comes from Frege’s concept “horse” problem (as well as the related difﬁculty inherent in Russell’s
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.29 How would Diamond reply to these objections? I suspect she would view them as placing a kind of pressure on her interpretation that it was not intended to bear: we could be seen here as fastening on to what is for her only a kind of rhetorical move in a polemic against a confused reading of the Tractatus. But while this account is suggestive and interesting. What is it about Wittgenstein’s supposed babbling that could so stimulate our imaginations. after all. even while insisting on its ordinariness. and direct them in such a particular manner? Or.Introduction fosters his metaphysical tendency. To demand from her an explanation of precisely how the plain nonsense of the Tractatus is illuminating could thus be said to miss the point: rather than seeking to provide an account of the mechanism of the text. We now can begin to see the real question that is opened up by Diamond’s work. if all we have at our disposal are his absolutely unintelligible strings of words. one still worries about its tendency to inﬂate the Tractatus’ notion of nonsense. her assimilation of metaphysical claims to “plain nonsense” is a means of denying the coherence of the notion of an ineffable content. one might wonder whether we can really make sense of Diamond’s notion of the “imagination” (a term. that does not play much of a role in the Tractatus). Diamond’s purpose is simply to steer us away from supposing any role for its propositions – after that “mechanism” has (somehow) performed its function. Diamond’s aim is not to provide a genuine characterization of Wittgenstein’s remarks.

indications of some of the elements of a proposed formalism – such as. p. So. is that despite Wittgenstein’s talk of employing a symbolism that “excludes” the “errors” of traditional philosophy (see TLP 3. For let us grant for the moment that Frege has a full awareness of the implications of the idea of extra-Begriffsschrift “elucidations.” Still. the absence of a sign for identity – with Frege’s systematic speciﬁcations in the Begriffsschrift and the Grundgesetze. while it is unquestionable that the notion of a canonical Begriffsschrift plays an important (if extremely unclear) role in the Tractatus. In other words. by always working within the conﬁnes of his formal language. But. the same language in which the nonsensical propositions of metaphysics were originally formulated.325).Introduction theory of types). We cannot confuse what are. to realize that Wittgenstein is shifting quite fundamentally the Fregean perspective. at best. once we understand that it is not embodied. But what is the domain in which Wittgenstein would have us operate. Frege’s (supposed) contention that certain prose judgments (the “elucidations”) can ultimately be transcended gains its force from the fact that one can operate perfectly well with his Begriffsschrift without ever making such judgments. a long tradition of Tractarian interpretation. in a formal
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. But it would seem to be of paramount importance at this point not to push the parallel too far. 8). it is equally certain that Wittgenstein has not actually provided us with any such language.30 The whole idea of an adequate notation can therefore only be part of Wittgenstein’s way of leading us to a new perspective on logic. then. a statement like “There are functions and objects” cannot even be formulated within his “concept script” – “∃f & ∃x” is not a well-formed formula – but the language nonetheless allows us to use these notions in the formalization of logical inferences. for example. of course. once we have dispensed with the elucidations that constitute the Tractatus? There is. The point. One might then describe the central problem that Diamond and Conant’s work points us toward as one of becoming clear on the nature of this perspective. it must be acknowledged that there exists for him a concrete means of avoiding the utterance of such statements – namely. as opposed to the adoption of an actual new language. going back to Russell’s Introduction to the book (TLP. at the end of the Tractatus we remain very much within the context of our “ordinary” language. for example. which views Wittgenstein as concerned with laying down conditions for an ideal language. as it were.

Let us then consider these three sentences:
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. as the appearance of the term “logical syntax” in the above purported exposition of the text’s central purpose should indicate. The problem now appears to lie not merely with how to characterize the text’s point – whether to describe it as the exposing of deep nonsense or plain nonsense – but with the very notion that we might “characterize” that point at all. How are we to characterize what the Tractatus brings us. Indeed. but a deeper underlying structure – what the text refers to as logical syntax (see TLP 3. if not impossible. in a speciﬁable method for eliminating the metaphysical pseudo-sentences. one will now maintain. They violate not ordinary syntax. the above claim will appear as a kind of reductio ad absurdum of the whole attempt to read this text. it may be tempting at this point to reach for a notion of “deep nonsense. garden variety sense.31 Still. 3. 3. I would urge that the situation is perhaps not quite so dire. position. 6.” The propositions of the Tractatus really are nonsense. while I by no means wish to downplay the peculiarity of the position in which we ﬁnd ourselves. is that we are from the start assuming that the statements proclaiming the nonsensicality of the Tractatus’ remarks could be true.325. is that perhaps Wittgenstein is concerned precisely to deny the possibility of such a neutral assessment of the nature of the text’s propositions. For the necessity of here bringing in the notions of the Tractatus itself – the very notions we have presumably “thrown away” at the book’s close – indicates the hollowness of supposing that we have. To some. This may seem to leave the would-be reader of the Tractatus in a difﬁcult. of the nature of metaphysical claims generally. one now begins to wonder about the coherence of even asking for an explanation in this context. What we are beginning to see. as yet. for Wittgenstein. we could say.334. however. We can then hold that it is just toward the recognition of the claims of all metaphysics as nonsense in this special sense that the text aims to bring us. to see? Given the difﬁculties that we saw above in the attempt to describe that insight in terms of the literal unintelligibility of the language of metaphysics. in the end. proffered any sort of explanation.33. The difﬁculty. a sentence like “ ‘The world is everything that is the case’ is nonsense” is itself nonsense. except not in the plain.Introduction language. What we are beginning to see is that. But this strategy is less promising than it may initially seem.124).

Introduction 1. like Frege.. then.” At the same time. the possibility of a general characterization of the text’s propositions is just to call into question the possibility of making straightforward assertions about “the meaning” of this predicate in the Tractatus. to emphasize that the term “nonsense” must be interpreted in the same sense in its second occurrence in (1) as in its ﬁrst occurrence within that sentence (i. we must recognize the very limited nature of this claim. 2. In an interesting way. it is to claim that an understanding of the term “nonsense” can only be attained through viewing in what Wittgenstein would regard as the appropriate way the (Tractarian) sentences to which it is appended. however. this description as yet tells us nothing about what those signs mean – precisely what any commentary on the text is presumably concerned to elucidate.
The appearance of paradox in (1) would seem to stem from the assumption that the terms that compose this sentence are all used in their ordinary senses – as if we were here committed to asserting the “plain nonsensicality” of the attempt to say anything whatsoever about Wittgenstein’s remarks. we must recognize how our capacity to make accurate statements about the Tractatus comes at the price of a restriction on their informativeness. ultimately having to ask for “a pinch of salt”. as we have. It is important. 3. “ ‘The world is everything that is the case’ is nonsense” is nonsense. as it occurs in (2)). Precisely this point is then expressed by (1): this sentence serves to reﬂect the reducibility within the Tractatus of (2) to (3). we understand what it means to ascribe this property to attempts to characterize statements of the Tractatus only to the extent that we understand the meaning of the predicate in the text itself. The world is everything that is the case. “The world is everything that is the case” is nonsense. But to deny. but rather as a meaningful and – I would claim – in fact true statement about Wittgenstein’s use of the string “nonsense. The sentence (1) is therefore not itself to be construed as somehow paradoxical. For while the above description of the role of certain signs in this text may be correct. the Fregean concept “horse” dilemma can be seen to extend not only to the Tractatus but also to any interpretation of the Tractatus: the commentator now ﬁnds himself in the position of. That is. however. he must
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.e.

in other words. but is rather given entirely in and through the recognition of an intrinsic instability in a particular kind of utterance. it is to admit that whatever is proposed as an answer cannot take the form that one will almost instinctively require of it. p. jump into Wittgenstein’s text.33 In different terms. but to face us back toward the text.34 It brings to the fore the extent to which we are. Indeed.32 My contention. is not to explain the meaning of the term “nonsense” in the Tractatus. That. we might say. that it cannot be understood apart from such a consideration. in putatively clearer terms. Nonsense. better. is as much as to admit that our central question about what the Tractatus brings us to see can permit no answer. It is now possible to describe in a new way Wittgenstein’s declaration of the nonsensicality of his own propositions at 6. engaged with the very metaphysics that is apparently being disparaged. Or. forms the lens through which all Wittgenstein’s propositions are to be viewed: we grasp his point just when we are inclined to understand these remarks as nonsense. of course. what this discussion helps to make evident is the fundamentally dialectical nature of Wittgenstein’s thought in the Tractatus. of philosophy generally. where Wittgenstein writes: “This book will perhaps only be understood by those who have themselves already thought the thoughts (die Gedanken) which are expressed in it – or similar thoughts” (TLP. 27). as it were.54. to begin using its language. of what we will claim to be Wittgenstein’s point. For while we can offer restatements. this dialectic can already be seen at the very beginning of the Preface. It is to suggest that the nonsensicality of Wittgenstein’s propositions only emerges through a detailed consideration of those propositions themselves. then.Introduction appeal to his reader to. to lead us to see that they must stand on the same level as the propositions of the Tractatus itself. it is contained in the seeing how our philosophical assertions change their character. is not expressible in some self-standing formula. how they undermine their own initial presentation as straightforward truth claims. But this. The appearance here of the meta12
. Rather than a neutral summing-up of the real purpose of the Tractatus. this remark would seem to function as a way of orienting us toward the text as a whole. the force of these considerations is to deprive such restatements of any privileged status. at every juncture of the book. of indicating how we are to read it. is that the Wittgensteinian view of the nature of his own claims.

we are deprived of a neutral standpoint from which to assess its ultimate nature. something that has nothing to with philosophy. that only someone who has reached the same “conclusions” as he will be able to understand the book. Given the emphasis of so much recent literature on 6. At 6. with the urge to transcend the bounds of sense.” as opposed to “a theory”).Introduction physically loaded. that his “demonstration” to his interlocutor will be of a fundamentally different nature than the “arguments” of the Tractatus. In fact. He is not suggesting. when someone else wished to say something metaphysical. one might well suppose that this remark was in fact the text’s ﬁnal statement. Fregean term Gedanke signals Wittgenstein’s intent. that Wittgenstein leaves us with his pronouncement of the nonsensicality of everything philosophical.” In the strict method. rather than being himself gripped by an urge to spell out a series of novel philosophical claims. But this does not mean that Wittgenstein’s claims in this context are now to be regarded as obviously sensical. though.
III
With the above in mind. we may come to say. i. as it may initially seem. Wittgenstein will then be clearly understood as responding to a particular kind of utterance. in contrast to the method of the Tractatus.e. i.112 calls “an activity. [one would] demonstrate to him that he had given no meaning to certain signs in his propositions.53. And that is to say once more that. the point is that these utterances have no purpose except for one who is genuinely tempted by the metaphysics it aims to explode. the Tractatus
13
. most empty – philosophical Gedanken. the propositions of natural science. insofar as we are engaged in this process (what he at 4. Rather. the metaphysical inclination of Wittgenstein’s interlocutor is open to view. Wittgenstein describes the “only strictly correct method” of doing philosophy as an enterprise in which one would say “nothing except what can be said..54.e. This same point is even more evident at the close of the Tractatus. What is regarded by him as “philosophy” will thus again necessarily involve the dialectical engagement with metaphysics. Wittgenstein’s “elucidations” depend for their effect on a prior yearning for the deepest – and therefore. and then always. we can begin to get a clearer sense of the nature of the “liberation” I have claimed the Tractatus aims to bring about.

thereof one must be silent. emphasis mine). then? We. that led Wittgenstein himself to go on with philosophy. then. since to do so would be to think what the Tractatus aims to reveal as not really thinkable. the dilemma inherent in the attempt to “draw a limit . . what is it exactly that we are not to say? Consider my own earlier references to Wittgenstein’s desire to preclude a “particular kind of utterance. It makes clear that the charge of “nonsense” against philosophy is not a claim alongside the claims of science but another move in the Wittgensteinian dialectic. an object. But if that dialectic’s purpose is to be achieved. of course. to the expression of thoughts” (TLP.54). for Wittgenstein. For the young Wittgenstein this aim is achieved by becoming clear on what he takes to be these utterances’ essence – the fundamental impulse that leads us to make them. That is: we do not know beforehand exactly what is to count as an illicit. ﬁnd their real fulﬁllment not in what we say. really is. it must ultimately culminate in its own cessation. Just this view of a unitary core to the
14
. Of course. Liberation. Wittgenstein’s own continued preoccupation with the problems of philosophy indicates how difﬁcult it can be simply to remain silent.” Wittgenstein’s claims. as we have characterized it. as by proclaiming. For assuming that our aim really was to cease speaking metaphysics. 27. want to say “philosophical” or “metaphysical” – but do we really know in advance the extension of those concepts? We are faced here with the essential difﬁculty of Wittgenstein’s dialectical enterprise. but in what we do.Introduction ends with proposition 7’s call for silence: “Whereof one cannot speak. is nothing other than the end of philosophy. more important. But it is not merely psychological compulsion that might lead us to continue – or. But this is precisely what is required by the text’s stance. if it is to lead us to “see the world rightly” (TLP 6. it would seem. the single question that he imagines to lie at their heart. . metaphysical claim. That is not to deny that the move is one of particular importance.”35 What kind of utterance. that the central task of the Tractatus is one of somehow delineating the class of those utterances it seeks to eviscerate.36 We could say. that the number 1 is. Wittgenstein’s ﬁnal remark brings out how we are in the end violating the spirit of the text every bit as much by proclaiming the complete and utter nonsensicality of metaphysics. we in fact cannot know this. p. for example. It might then seem that we would best make the Tractatus’ point by stopping our commentary right here.

” “show. have their life only within the text. Now this whole line of thought may sound suspiciously reminiscent of the uncharitable reading of Cora Diamond’s notion of transitional remarks – as if I were suggesting that Wittgenstein’s remarks ﬁrst make some sort of sense and then subsequently become nonsensical. To read the Tractatus dialectically. But that is to say that the Tractarian commentator’s task is and must be enormously complicated: the successful interpretation will have the same “logical multiplicity” (to borrow a phrase from the Tractatus) as what it expounds. Wittgenstein writes: “Philosophy unties the knots in our
15
.
IV
This conception of the aim of the Tractatus both clariﬁes and complicates the task of its would-be interpreter. as well as others). is to recognize that the successful characterization of philosophy is its dismissal as Unsinn. one might say that we are engaged in an act of translation rather than one of explanation. philosophically neutral claims about these notions is to mislead (ourselves.Introduction problems of philosophy is expressed in Wittgenstein’s audacious Preface claim to have found “on all essential points.” like the rest of the terms of the Tractatus. in my sense of the term. that to seek to make general. in fact. or of how we can purport to explain what Wittgenstein holds can only be shown. p. Our task as commentators is then precisely one of describing. for Wittgenstein. it is a search for the liberating word. as accurately as possible. the root of the drive toward metaphysics. in which Wittgenstein twice speaks of the sense that his seemingly multifarious investigations are all manifestations of a “single great problem” (see NB 23 and 40). 29).” “explain. The same idea also appears in the Notebooks. the revealing of the essence of metaphysics and the “demonstration” of the nonsensicality of metaphysics are. Wittgenstein’s enterprise is an attempt to lead us to a view of metaphysics so complete that it dissolves itself. in that we now see that we need not tie ourselves up in knots over the question of how the text’s nonsense can be illuminating. the[ir] ﬁnal solution” (TLP. it must be as complex and multifarious as the text itself. We recognize instead that “nonsense. two sides of the same coin. The Tractatus is then really nothing but Wittgenstein’s extended attempt to characterize that single great problem. I believe. In the Philosophical Remarks. But my claim is that. the role of those terms. It is clariﬁed.

Chapter III will inquire into Wittgenstein’s understanding of logical inference. which we have tangled up in an absurd way. all the main “topics” with which this text is typically taken to be concerned. ideally. This remark holds for the task of Wittgenstein’s would-be expositor as well.174–2. his speciﬁc response to the logic of Russell’s Principia Mathematica and Frege’s Begriffsschrift and Grundgesetze. but to do that. the propositional attitudes. Although the result of philosophy is simple. however. to address. general principles that we can invoke in order to understand the Tractatus – only the arduous task of working our way through its many intricate details. we shall involve ourselves in just such a close textual analysis. we have ignored what Wittgenstein declares.Introduction thinking. it seeks to be comprehensive.063) and their connection to the ﬁrst part of the picture theory (TLP 2. no simplifying. And while I would hold that the key ideas motivating Wittgenstein’s way of handling the propositional attitudes and solipsism will at least be familiar by the end of our study. its methods for arriving there cannot be so” (PR 2). In our focus on questions concerning the logic of the Tractatus. Chapter II will focus on the notion of analysis.1–2. scientiﬁc theory.172). the Tractatus’ fundamental notion of the “general form of the proposition. In the interest of readability. the discussion of “sense” in the 4s and 5s. “ontological” remarks (TLP 1–2. in a famous letter to von Ficker. There is another important issue that has been conspicuously absent from our discussion thus far. this study falls somewhat short of this ideal: in particular we shall have to ignore or give short shrift to the Tractatus’ discussions of number. In what follows. probability. Thus. ﬁnally. to be the text’s real purpose
16
. and. we can hope to justify the omissions by attempting to convey (what I would claim is) the chief import of these discussions through our account of the Tractarian notion of the sense of a proposition. as it is presented in the 3s and early 4s.” Our approach to the Tractatus will aim to reﬂect as far as possible its author’s view of the uniﬁed nature of the inquiry that it represents. at least to some extent. Here we shall focus on the last part of the picture theory (TLP 2. they be given independent treatment. Chapter I will discuss the opening.225). and of solipsism. In the ﬁrst three cases. the importance generally accorded to these notions would demand that. it must make movements that are just as complicated as the knots. There is no shortcut.

like its English counterpart. Wittgenstein himself uses a cognate of this word in connection with a discussion of the meaning of Christ’s Resurrection.37 Indeed. There are. is properly an internal feature of philosophical inquiry.39 It seems. These concern the inevitable demand for a more complete justiﬁcation of our approach to the Tractatus. We must come to see the dialectical grappling with the limits of sense as a fundamentally ethical struggle. the expression of an “ethical” point.Introduction – namely. for Wittgenstein we must come to understand in a new light what we’ve already been doing in reading this text.
V
One further set of questions needs to be addressed before we turn to the details of the text. but only to bring out explicitly what. The attempt to make apparent this dimension of Wittgenstein’s thought will occupy us in the last chapter of this book. doesn’t our approach have the consequence of collapsing the distinction between the early and later thinker – the distinction that Wittgenstein himself time and again remarks on?
17
. Why must we take the difﬁculties in rendering the text coherent (discussed in Section II) to indicate the need for reading it in the dialectical manner that is here being urged? Is it not just this kind of incoherence that motivates the fundamental shift in Wittgenstein’s thought? Indeed. then. implies that this aspect is something that is supposed to be made manifest by the text as a whole.38 One cannot but then wonder what place this sort of concern could occupy in the text as we have presented it thus far. after all. carrying the sense of something that saves or redeems us. just such a dimension is implied by our suggestion that the Tractatus is essentially an attempt to “liberate” us from a particular sort of confusion: the word erloesend. Our aim here will not be to sum up and explain the “real meaning” of the text (although the temptation to do so will be especially strong at this point). for Wittgenstein. Wittgenstein. has an explicitly ethical or religious connotation. that rather than viewing ethics as an additional subject matter treated by the Tractatus. of course. But I believe it is a mistake to seek to locate the ethical aspect of the work solely or even primarily in these remarks. the relatively small number of remarks toward the end of the Tractatus that explicitly address religious-sounding themes.

On the contrary. through its ability to deal with the details of the text in a compelling manner. Why would Wittgenstein be concerned with such details if he were truly committed to the ultimate nonsensicality of the questions at issue?40 But I believe that we are here presented with a false
18
. the honest answer is a perhaps disappointing one: nothing ultimately compels one to read the Tractatus in the way that I maintain. is not to claim that such an ability functions as a criterion of our interpretation’s adequacy. For it is quite reasonable to demand that a comprehensive interpretation be able to accommodate Wittgenstein’s many post-Tractarian references to shifts in his thinking. it cannot be entirely convincing. however. in general. one of the subaims of this study is just to shed some light on this whole issue. to render the whole coherent.Introduction To the ﬁrst question. I do not take to be a shortcoming of my particular approach. that Wittgenstein himself would insist on). I am simply saying that. must wear its persuasiveness on its face. the very speciﬁcity of these criticisms has led many commentators to understand them as revisions to a general philosophical theory. but a feature of any interpretation of a philosophical work (a point. the nature of analysis. The other objections must be met more forcefully. like any textual interpretation.” The legitimacy of our own particular approach can then only be established – or fail to be established – in a wholesale manner. These criticisms do not take the form of a global reassessment of his overall philosophical aims but. and so forth. Let me be clear. Of course. shifts in his understanding of rather speciﬁc points – the analogy between a proposition and a picture. that I by no means wish to downplay the signiﬁcance of Wittgenstein’s claims to have changed his mind on various matters.) Rather. (The assertion that a reading is acceptable because it renders the text more coherent is really no more than a grammatical remark in the sense of the later Wittgenstein. in the end. That. of course. I believe. then. if our reading has the consequence that such remarks must simply be dismissed. is that Wittgenstein’s later self-criticisms are to be understood as the recognition in his own thinking of the very philosophical demons the Tractatus had sought to completely exorcise. What I shall seek to show. rather. For at issue are fundamental intuitions about what kind of thinker Wittgenstein at bottom really is – not straightforward “mistakes” settled through the production of “proof text. This. our interpretation. the role of the quantiﬁer.

19
. from what we have said above it might already be apparent just why this is the case – that is. And while these points about Wittgenstein’s development will in general be made in the footnotes. why matters of detail will loom large for Wittgenstein.Introduction dichotomy. we shall then address some of these later corrections. the assertion that such and such a claim does not make sense is related internally to the particular way its incoherence is made manifest. we shall be immersed in very close textual analysis of the Tractatus. even while his fundamental philosophical orientation remains the same. “nonsense” is not a general or self-standing predicate for the Tractatus. In the course of this study. To misdescribe the philosophical problem is in a sense to miss the point – Wittgenstein’s own (real) point – entirely. then a precise characterization of the nature of that incoherence is all-important. much will therefore be at stake in eliminating what he comes to regard as the distortions in the Tractatus’ presentation of the appropriate perspective – hence the dire character that he often attributes to the “errors” in his early thought. that is. indeed. For if.41 For Wittgenstein. I believe it to be very much in the spirit of the philosopher at the center of our study. and seek to understand them in light of our reading of the Tractatus. it is to propagate the very confusions from which Wittgenstein aims to liberate us. if. the issue of the interplay between the early and late philosopher instead informs our reading throughout. In what follows. The focus required to work through the internal intricacies of this difﬁcult text will preclude our offering a great many remarks as we go along about the broader project in which Wittgenstein is engaged. And while I recognize that this sort of approach places a high demand on the reader. will emerge through the details. one hopes. that broader project. this should by no means be taken as indicating their lesser importance. as I maintain. And.

.

perhaps. For at 5. when its implications are followed out strictly. “Realism” and “solipsism” (a term that.64). What is the stance of the Tractatus? From what position are its absolute pronouncements made? One might suppose that such self-reﬂective questions would have little relevance to the opening of the Tractatus. followed by the qualiﬁcation: “The world is the totality of facts (Tatsachen). however. beyond proof. The text at this point looks entirely outward. We do not at once know why they have been offered up. 28) – beyond reproach it seems. we must recognize that this cannot itself be an unself-conscious move on his part. is often
21
. for Wittgenstein.CHAPTER I
PICTURES AND LOGICAL ATOMISM
I
The Tractatus opens with the famous declaration: “The world is everything that is the case” (TLP 1). coincides with pure realism. after denying that there is an “a priori order of things. or what the basis for asserting them might be. If that is the case. The self of solipsism shrinks to a point without extension. One is immediately struck by the dogmatic. on to the world. any concern with the conditions of its own utterance apparently falls outside of its purview. as “unassailable and deﬁnitive” (TLP p.” he remarks: “Here it can be seen that solipsism. absolutely authoritative tone of these claims. not of things” (TLP 1. so to speak. They present themselves. It is as if the author of the Tractatus were completely absorbed into the external reality that is here described – as if Wittgenstein were. but also.1). presenting a realist’s perspective purely realistically.634. and there remains the reality co-ordinated with it” (TLP 5. in the words of the Preface. nor will any later justiﬁcations be provided.

This suggests not only that it can make no sense to speak of anything beyond logic but also that it makes no sense to speak of new domains within logic. this text from the very beginning brings such questions to the fore. referring to the very activity in which he is engaged: the Tractatus is itself a logical inquiry. already be present to us.012). While a scientiﬁc investigation seeks to determine what is the case. And that suggests that. The occurrence of the word “logic” at 2. The limits of logic are the limits of the possible. A book on logic should not then contain arguments. as it were. and all possibilities are its facts” (TLP 2. Wittgenstein is not here describing a subject from afar but. This already begins to throw light on the reasons for the text’s peculiar. logic deals only with the possibility of what is the case. Logic deals with every possibility. of logical discoveries. rather. as well as the ﬁrst part of
22
. would appear to be essentially different from a scientiﬁc investigation.012 and 2. in some sense. rather. “Nothing in the province of logic can be merely possible. The apparent dogmatism of the Tractatus reﬂects just the utterly uncontroversial nature of the subject with which it deals. far from dismissing all questions about the nature of its own stance. to equivalent ways of describing the world.Wittgenstein’s Tractatus used synonymously with what we would ordinarily call “idealism”) do not refer to competing philosophical positions but. to present things in such a way as to allow us to. Unless we are to imagine him to shift radically his thinking in the course of the book.1 Instead. recall what we already know. The full expanse of logic must. as Wittgenstein conceives of it. For a logical inquiry. the perspective it adopts is the perspective of logic.0121). “In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing” (TLP 2. The aim of the present chapter is then to bring out how the Tractatus’ “ontological remarks” (TLP 1–2. Rather.0121 would then appear to be signiﬁcant. as if it described novel facts about whose existence we had to be convinced.063). one’s only concern can be to lay matters out perspicuously. Wittgenstein cannot then be understood as at the start straightforwardly advocating a realist stance in opposition to some other philosophical position. seemingly dogmatic style. it seems more accurate to see the opening as one means of characterizing or exemplifying a perspective: the Tractatus is attempting to adopt completely a certain way of looking at the world in order to make manifest what that outlook comes to.

Given the above
23
. . our description must incorporate within it some acknowledgment of structure. as Mounce suggests. or that it serves. indeed.” to begin to make fully evident the real character of a logical inquiry. and it is this that will represent our concern as well. for Wittgenstein (or. insofar as it is put forward in the service of something like a Fregean project of spelling out the “laws of thought. not things. it must see the world as composed of facts.
II
We can now begin to reﬂect in more detail on the fact/thing distinction with which the text begins. in a later conversation with Desmond Lee. as we shall see. Instead.Pictures and logical atomism the picture theory. a few scattered comments notwithstanding. offers this interpretation of the Tractatus’ opening remarks: “The world does not consist of a catalogue of things and facts about them (like a catalogue of a show). What the world is is given by description and not by a list of objects” (CL 119). logic consists in. only to delineate how the world must be if there are propositions and hence the possibility of logic?2 While these suggestions may sound tempting. mathematical logic is critiqued only insofar as it answers to the interests of logic in the broader sense – that is. the Tractatus does in one sense distinguish mathematical logic from the attempt to give a broader account of that endeavor: this distinction is reﬂected in the text’s application of the term “senseless” (sinnlos) to expressions of the form “p v p. We might imagine a world consisting of objects a and b and a relation R. Now such an interpretation might seem difﬁcult to sustain.”3 Nonetheless. Frege’s Begriffsschrift or Russell’s Principia Mathematica – is not treated by Wittgenstein until the 3s or even the 4s. .” but “nonsensical” (unsinnig) to expressions like “p is a proposition. as it is systematically presented in. . If our aim is to describe accurately this world. To be sure. given that. say. it is not enough simply to offer a list of these constituents – this list would not distinguish a universe in which aRb is the case from one in which bRa is the case. I claim that they rest on too narrow a conception of what. serve to clarify this “uncontroversial subject. for Frege and Russell). Wittgenstein.” It is always this inquiry into the fundamental possibilities of sense and nonsense that is of concern to Wittgenstein in the Tractatus. Should we not then say that the early discussion is merely preparatory. “logic” as we ordinarily conceive of it – that is.

that while the primacy of facts may not preclude all talk of objects. “What is the case. it would seem. and everything else remain the same” (TLP 1. through looking at a series of facts with an eye to what is common to them. then.21 states (and 2. as becomes apparent when we reﬂect on the above conception of logic. Whether fact A obtains or does not obtain is then a contingent matter that is irrelevant to the perspective of the Tractatus. “fact” and “object” must be seen as standing at different levels: one’s hold on the notion of an object comes through a way of approaching what is the case. the condition of its possibility. however. To identify the objects is then not literally to further decompose the world but. Instead.4 Indeed.061 reiterates). one might otherwise wonder how the original primacy of fact over thing is to be maintained. then it appears that the world is. the fact (Tatsache) is the existence of atomic facts (Sachverhalten) (TLP 2). or temporal objects apart from time. so we cannot think of any object apart from the possibility of its connexion with other things. the obtaining of Tatsachen as such.0121) If I know an object. For as 1. composed of things not facts after all. it would appear that the focus of logic cannot be on this structure. For. with what conditions their obtaining or not obtaining. It is in connection with this idea that the notion of the object (Gegenstand) must initially be understood. Logic’s concern. given what is held at 2 and 2. The difﬁculty is that if these remarks are taken to mean that a fact is made up of atomic facts and an atomic fact is made up of objects or things or entities (Wittgenstein makes it clear here that these terms are interchangeable). 24
. If I can think of an object in the context of an atomic fact. An atomic fact is a combination of objects (entities [Sachen]. the notion of possibility is bound up with the Tractatus’ initial account of the object:
Just as we cannot think of spatial objects at all apart from space. (TLP 2. at bottom. rather. things [Dingen])” (TLP 2. It would seem. neither can the latter be understood as a more basic constituent of the world.21). we are back to conceiving of reality as describable by a list. then I also know all the possibilities of its occurrence in atomic facts.01. must only be with the possibility of the Tatsachen. to seek to grasp its logical basis.01). I cannot think of it apart from the possibility of this context. facts are logically independent of one another: “Any [Tatsache] can either be the case or not be the case.Wittgenstein’s Tractatus discussion.

insofar as it can occur in all possible states of affairs. to suggest that the Tractarian object must therefore be understood as dissolving simply into a possibility – as if we could understand the condition of the world apart from any consideration of how things actually stand. It is constitutive of the object to occur in an atomic fact.” But while Frege goes on to contrast this idea of a as “2( )3 “dependent” function with that of an object as a self-standing entity. he suggests that the real nature of the function could be made apparent through the use of blank spaces for the argument place of a functional expression. etc. one that is a “whole complete in itself. the object is this thing taken against the background of all the rest of its possibilities of combination with other things. as 2. as well as his ﬁrst-order functions.” predicative entity that combines with it. a form of dependence” (TLP 2. He emphasizes the way in which the function does not stand on its own but is instead given by looking to what is common to a series of propositions. In this vein Wittgenstein remarks: “The thing is independent. Frege famously draws a distinction between the object and the function – roughly.” then the object is not form alone. too. Of course.5 It is useful to compare this conception of the object with Frege’s.033 suggests. the object is understood just through its appearance in a whole series of facts and in this sense can be said to represent the “possibility” of any one of them. but this form of independence is a form of connexion with the atomic fact. both function and (Fregean) object must be equally understood in terms of their capacity to occur in a space of facts. are objects too” (NB 61). both form and content.0123)
The point might be put as follows. It seems that we should then say that Wittgensteinian objects comprise Frege’s objects. as the “possibility of structure. since these Fregean categories are set up in such a way as to be applicable to anything whatsoever that
25
. and so forth. (TLP 2. Thus. second-order functions. between that which corresponds to a proper name and the “unsaturated. If “form” is understood. but not only in this fact. but.0122).025. however.) A new possibility cannot subsequently be found.Pictures and logical atomism
(Every such possibility must lie in the nature of the object. Instead. as when the expression “2x3 x” is written ( ). he asserts in the Notebooks: “Relations and properties. just as is stated of substance at 2. This is not.”6 the Tractatus’ aim would seem to be to bring out how no genuine logical distinction could be drawn between these notions. Thus.

It now begins to become apparent that Tractarian objects defy easy integration not only into a Fregean framework. a claim with no content.” Thus he remarks:
Two objects of the same logical form are – apart from their external properties – only differentiated from one another in that they are different. it would appear to be the reverse: rather than seeking to understand objects in terms of some prior philosophical category. or. and then it is quite impossible to point to any one of them. that objects are not merely form. and then one can distinguish it straight away from the others by a description and refer to it.7 Wittgenstein will not allow us to rely on any such categories as basic. Still. but both form and content. even in principle. but also into any sort of traditional philosophical framework.” “universal. this formulation is misleading. For if a thing is not distinguished by anything. Indeed. (TLP 2. (TLP 2.02331)
We have no way of establishing the identity of an object except through its particular capacities to combine with other objects. But insofar as putting matters this way makes it appear that Wittgenstein is riding roughshod over Frege’s more ﬁne-grained distinctions. this cannot be altogether incorrect. the Tractatus is suggesting that it is
26
. For it is essential to recognize that the Tractatus is not at the start attempting to tell us what sorts of things there are.” or “sense datum” to try to make sense of what he has in mind. On the contrary. While we will no doubt be tempted to bring to bear notions like “particular. To attempt to differentiate two objects with the same logical form is to do no more than to make a bare assertion of difference. though.Wittgenstein’s Tractatus can be said about the world. that which 2. Wittgenstein’s emphasis on combinatorial possibilities is meant to question the coherence of such a priori categorization: what a given object is is only determined by the speciﬁc range of its occurrences in atomic facts. one might wonder how the question of separating two objects of the same logical form could initially arise. on the other hand. to introduce the notion of an object is not yet to have identiﬁed a logical kind. I cannot distinguish it – for otherwise it would be distinguished. there are several things which have the totality of their properties in common. as clariﬁcatory. Would this not be like trying to ask whether this desk might be distinguished from itself? We again recall.0141 calls the “form of the object.0233) Either a thing has properties which no other has.

It is important to compare what that remark says about the notion with 3. Such simple objects constitute the substance of the world.02–2.24. a claim that closely parallels 2. we might say.8 With this point in mind. a primitive notion.02) Every statement about complexes can be analyzed (zerlegen) into a statement about their constituent parts. and into those propositions which completely describe the complexes. A complex can only be given by its description.” we must then approach this passage with some care.Pictures and logical atomism only through their possibilities of occurrence that those fundamental categories emerge.9 It is useful to quote this difﬁcult passage in its entirety:
The object is simple. logical atoms comprise particulars. (TLP 2. and this will either be 27
. a process that is imagined eventually to terminate in entities entirely lacking in complexity. (TLP 2. he assumes the possibility of engaging in a process of logical analysis. Wittgenstein could well seem to be adopting some variety of Russellian “logical atomism. is essentially concerned to call into question the legitimacy of this kind of a priori logical categorization. If we are to bring out the real force of the Tractarian “argument for simples. then whether a proposition had sense would depend on whether another proposition was true. The object is. relations.0211) It would then be impossible to form a picture of the world (true or false).0201) Objects form (bilden) the substance of the world.0212). its necessarily existent logical core.021) If the world had no substance. Let us ﬁrst focus on the idea of the “complex.” Like Russell in The Philosophy of Logical Atomism. (TLP 2.0212)
If we take these remarks on their face. a series of remarks that has received a good deal of treatment in the literature.0201:
A proposition about a complex stands in internal relation to the proposition about its constituent part. A very different conception of simplicity would thus appear to be operating in the Tractatus. (TLP 2.0201. But whereas Russell is then naturally led to specify the nature of these endpoints of analysis – for him.” which appears in 2. (TLP 2. we can then begin to understand the socalled argument for simples (2. and qualities – Wittgenstein. Therefore they cannot be compound. we have just suggested.

The complex. though.24)
In holding that a statement about a nonexistent complex is false rather than nonsensical.0201. Now a more complete account of exactly what procedure he has in mind at this point must await our discussion in the next chapter. Wittgenstein maintains there that a proposition about a complex can be analyzed into a statement about that complex’s constituents. from a logical perspective. one whose composition is essential to its nature. the very possibility of describing such an entity shows that it is really not an entity at all. if some complex C were imagined to be an entity literally made up of simple objects a and b. so to speak. in other words. on completion of an analysis) absorbed into a series of propositions. if this does not exist. is ultimately (i. Already. implies at the very least that analysis must involve something other than a process of decomposing complex objects into their basic constituents. Instead. Again.12 But if complexity is in this way always associated with the holding of facts. The proposition in which there is mention of a complex.13
28
. To make that distinction evident can now be seen to be the central purpose of 2. as one kind of entity among others in the world. then.0211. but a structure – the obtaining or holding of entities. becomes not nonsense but simply false.11 For Wittgenstein.0211 holds that the existence of objects is a condition of the possibility of sense.. this remark can be seen to bring out how the complexity of the complex. After all. that runs counter to 3. the apparent “reference” to a complex in the unanalyzed proposition marks a disguised allusion to a fact or set of facts. and this statement into a number of propositions that then completely describe that complex.e. is not to be treated. then the proposition that makes mention of (nonexisting) C becomes nonsensical.Wittgenstein’s Tractatus
right or wrong. we are led to draw a fundamental distinction between the complex and the object. then C’s nonexistence would entail the nonexistence of a and b. And while we are by no means yet in a position where we can discuss in detail the Tractatus’ conception of analysis. when taken together with 2. though.10 this claim.24. (TLP 3. it then would appear that the object cannot but be simple – that there are no logical objects or entities other than simple ones. By beginning to reﬂect on what it would mean to give an analysis. Wittgenstein is saying that the existence of that complex is irrelevant to the statement’s sense. But since 2.

021 that objects as the substance of the world “cannot be compound. a colored object. logic.” must ultimately be understood as suggesting that predicating complexity of a logical entity can make no sense. A name designating an object thereby stands in a relation to it which is wholly determined by the logical kind of the object and which characterizes that logical kind. I call some rod “A” and a ball “B. logical core. Wittgenstein. views the world always through the lens of simplicity. For this is just to maintain that an object shorn of some of its combinatorial possibilities – that is. e. indeed. So. Wittgensteinian analysis must then be seen purely as an attempt to describe the world in such a way as to render perspicuous its simple. If we are to adopt the point of view of logic. as far as logic is concerned. Wittgenstein remarks in the Notebooks:
If.Pictures and logical atomism And. on reﬂection. Solely from the functioning of the name “A” in the elementary proposition
29
. it is assumed that the identity of the object. For Russell. that is. the goal of logical analysis is to specify the sorts of objects that satisfy certain conditions: we identify the genuine simples when we distinguish from complex entities those objects that are incapable of deﬁnition and are instead known only by direct “acquaintance. it could not have any such form and remain A. Thus. say. or something with a weight.” I can say that A is leaning against the wall. but not B. for example. Here the internal nature of A and B comes into view. we might say. an object that is further decomposed – will no longer be the same entity. though. perhaps.. if “A” in the passage above were a genuine name. then A would appear in the atomic fact as leaning or even. but rather to reveal clearly the logical role or function of that which is before us. our proper aim is not to seek the right kinds of entities. it must then be evident from the role of the name in any given context alone just what the object it designates is – no additional contexts of its occurrence need be considered. in holding at 2. The contrast of the Tractatus’ logical atomism with the Russellian version thus becomes striking. is determined by the possibilities of its occurrence in a series of atomic facts.
Again.” In the Tractatus. we see that this point follows from the conception of the Tractarian object as constituted by its possibilities of combining with other things. as leaning against a wall. It could not also occur as.g.

24 maintains that a proposition that makes mention of a nonexisting complex is false rather than nonsensical. as 2.Wittgenstein’s Tractatus representing that atomic fact. Notice. he claims. We now can begin to see why Wittgenstein insists on the existence of that “substance” that the simple objects are said to form or constitute. we would not be able to say that. The denial of substance. And in this case. 3. given the Tractatus’ conception of the object. what here would be suggested is that a whole space of possible occurrences might not be given. but that the argument place itself. In Fregean terms. were not available. This is just to say that if the possibilities of representation were not already secured in advance. then. Wittgenstein suggests that it is nonsensical to imagine such a possibility. To deny the existence of substance is to call into question the very possibility of the representation of atomic facts. Without the givenness of objects. as some commentators have suggested. the reason for this claim becomes apparent: the nonexistence of a complex is equivalent to the nonobtaining of a fact or series of facts. true or false. it would be impossible to form a picture of the world. As we saw above. an inﬁnite regress would then ensue. But since the proposition expressing that knowledge would be subject to the same indeﬁniteness of sense. the essential nature of this object becomes manifest. turn on a worry over the holding of the connection
30
. it would always be an open question as to whether a given fact could be represented.0121 maintains. In denying that a genuine name has reference. If we understand talk of a “complex” as reﬂecting the confusion of a gesture toward a structure with a reference to a logically compound entity. that the point here does not. Instead. it would be as if one were to suppose not that a function did not hold for some argument. we are not raising the possibility that one occurrence of an object does not exist – that is simply to imagine the nonobtaining of some atomic fact. is tantamount to making the sense of a proposition dependent on the truth of another proposition. the possibility of an argument. A is leaning against the wall until we ﬁrst knew that A was the kind of thing that was capable of occurring in this context. But the situation is otherwise with regard to an object. For what would it mean to suppose that there might not be objects in this sense? It is useful to compare such a scenario with the possible nonexistence of a complex. for example.

In other words. that logic is. the existent. But from the above preliminary points about analysis. the real concern is with the fundamental ascriptions that can be made to the world. But the above discussion does allow us to gain a better grasp on the notion of the atomic fact:
The object is the ﬁxed. from a logical perspective. For Wittgenstein. instead. Now. the variable.Pictures and logical atomism between the name and the object – as if Wittgenstein were claiming that. without a guarantee of immediate contact between language and the world. (TLP 2. like the links of a chain. it would seem that this nature (the form of the object) should nonetheless at least be evident through any one of those occurrences. the conﬁguration is the changing. as it were. the possibilities that allow the facts to stand in the way they do. self-subsistent. it would never be certain as to whether our names really did refer.0272) In the atomic fact objects hang in another. what. the particular way that the object does lie in the atomic fact must reveal clearly just how it can lie – which is to say.15 It is just this idea that is expressed in the characterization of substance as “what exists independently of what is the case” (TLP 2. (TLP 2. this tension only begins to resolve itself in the account of the picture. it is not yet clear how this claim about the need for the logical possibilities of the world to be given in advance coheres with what we have said to be Wittgenstein’s questioning of any attempt at a priori logical categorization.032 terms the “structure” of the Sachverhalt. To say that these objects hang in one another like the links of a chain is to emphasize that no further elements are involved in this conﬁguration.14 No such problem of reference is at issue in the Tractatus. it
31
. since the identity of the object is determined by all its possibilities of combining. The requirement for substance is ultimately nothing but the insistence that nothing underlies or conditions logic. no additional “relations” to bind together its components: the atomic fact is constituted solely by the objects being arranged in this way. any single occurrence of an object – any particular way of its hanging in an atomic fact – does not exhaust its nature. (TLP 2.024). That particular arrangement 2.03)
The atomic fact is in its essence an arrangement of objects.0271) The conﬁguration of the objects forms the atomic fact. the structure thus consists in how the objects hang together. Of course.

the concern that occupies the text from that point on. the introduction of the picture represents the Tractatus’ shift from ontology to the concern with language. the central aim of the subsequent discussion of the picture to bring that question – the fundamental question of logic – into sharper focus. I claim. indistinct. And that would suggest that. whose picture the proposition is. already.” For it would appear that. it must be acknowledged that the real nature of the question that the Tractatus is pursuing remains at this point abstract. it would seem. even in the atomic fact. emerging through the structure. Certainly the Notebooks does not recognize a sharp distinction between an investigation into the proposition and an investigation into the world: “My whole task consists in explaining the nature of the proposition.” The atomic fact. such an interpretation runs counter to the standard way of approaching the “picture theory” (so-called). then. At the same time. however. the Tractatus is leading us to call into question the fundamental supposition of the thought of Frege and Russell – the supposition that logic constitutes a genuine science. its necessarily existent core. the inquiry into substance seems ultimately to represent no more than a perspective on the world.17 But while it is undeniable that the notion of the picture is meant to shed light on the proposition – propositions are explicitly described as pictures at 4. It thus becomes apparent that the requirement for objects and the postulation of atomic facts are closely linked.16 Of course. Similarly. substance is presented only indirectly. are demands of the logical inquiry itself. 2. both. presents its structure precisely in such a way as to make the forms of its constituents manifest. reﬂection on this idea begins to reveal the peculiar nature of the inquiry into that “existent core.Wittgenstein’s Tractatus essentially is.01 – it is not so clear that such a focus represents a genuine departure from the focus at the opening of the text. several remarks in the Tractatus appear to emphasize how the
32
.033 describes “form” as “the possibility of structure. Still. On the standard view. a way of viewing what is the case. through the way in which things stand. In giving the nature of all being” (NB 39). Rather than constituting an ordinary subject with its own special area of concern. It is. in giving the nature of all facts. one could say. That is to say. To postulate the possibility of describing what is the case (the totality of Tatsachen) in terms of the existence of atomic facts is simply to suppose the possibility of a perspicuous presentation of the logical dimension of the world.

we might have assumed that the totality of existent atomic facts constitutes the limit of the world. a clariﬁcation of the same inquiry that is initiated at the start.” In 2.” then comes as a surprise: “The existence and nonexistence of atomic facts is the reality” (TLP 2.0131)
Indeed. alone and in the proposition. object.0s. (A point in space is an argument place.
III
In keeping with this overall approach. all that is the case with the totality of facts (TLP 1.” a notion with an apparent wider extension than “the world. For it is very tempting
33
. we note the seemingly shifting sense of the term “world.0122) A spatial object must lie in inﬁnite space.1). And this suggests that rather than marking a sudden shift in the direction of the text. a form of dependence.) (TLP 2. when we reﬂect on our own interpretation of the opening passages. But it would also seem to blur the Tractatus’ fundamental distinction between the fact as what happens to obtain and the object as its logical condition.Pictures and logical atomism text’s early claims about the world can be interchanged with points about language:
The thing is independent. Given the text’s initial association of the world with all that is the case (TLP 1). Is Wittgenstein imagining atomic facts that lie outside of the world? The idea is in itself strange enough. The subsequent introduction of the term “reality. in so far as it can occur in all possible circumstances. “the world” is identiﬁed with the totality of existent atomic facts (die Gesamtheit der bestehen den Sachverhalte). First.06. the account of the picture is really only a deepening.04. but this form of independence is a form of connexion with the atomic fact. we can then understand the introduction of the notion of the picture as immediately motivated by certain tensions in the remarks that close the 2. italics mine). and this totality with the existence of atomic facts (TLP 2). we note how it also has been bound up with linguistic notions – how the notions of fact. and atomic fact have been explicated only through talk of propositions and names. (It is impossible for words to occur in two different ways.) (TLP 2. This intertwining of the putatively independent notions of language and world would thus seem to be intrinsic to the Tractatus’ understanding of the logical perspective.

but then feel driven to posit possible objects (possible possibilities as it were) as the logical bases of these nonexistent. is that we cannot view positive and negative atomic facts as separate or independent notions: we can infer the nonexistence of A from the existence of A (A “determines” A) just because. The just introduced distinction between “reality” and “the world” is now apparently denied or in some sense overcome.37). however. then.” as Wittgenstein refers to the nonexistent atomic fact at 2. This assertion. Or. we run up against the intrinsically ambiguous status of what is not.062).06s. Once more. Why this equivocation? What is the status of the “negative fact.06 provided by 2. the Tractatus would seem both to propose the existence of facts outside of the world and to imply that such an idea doesn’t make any sense. would seem to run counter what is maintained just three remarks previously: “The totality of existent atomic facts also determines which atomic facts do not exist” (TLP 2.21s claim of the logical independence of facts. we may maintain the distinction between a fact and its condition.0s centers around the question of the relation between atomic facts. some version of the ancient problem of the nature of “what is not” that confronts us at the close of the 2. in keeping with the 1. At 2. Wittgenstein claims: “From the existence or nonexistence of an atomic fact we cannot infer the existence or nonexistence of another” (TLP 2.062. A does not count as another fact. equally complicating matters. it then seems.063: “The total reality is the world” (TLP 2. There is only logical necessity” (TLP 6. merely possible facts. A second tension in the remarks ending the 2.Wittgenstein’s Tractatus to view the nonexistent atomic fact – the fact that is not but could be – as in some sense another condition of the possibility of the (existent) atomic fact. But that would ﬂy in the face of 6. One wonders how one set of facts can “determine” a second set if these facts are entirely independent of each other. it would seem. It now appears that this difﬁculty is connected with the notion of logical inference: the possibility of logical relations
34
. The solution. Wittgenstein’s position becomes still more puzzling when we look at the supposed further clariﬁcation of 2.063). It might be tempting to suppose that Wittgenstein is introducing the possibility of a relation of determination distinct from one of logical inference. from the perspective of A.37: “A necessity for one thing to happen because another has happened does not exist.05).06? It is.

the existence and nonexistence of atomic facts (Sachverhalten)” (TLP 2. To speak of a measuring-rod is of course to speak of something that cannot be understood apart from its connection with human purposefulness – presumably no one will suppose that a ruler might apply itself to the object to be measured. but rather as something to be viewed within the context of its use. then. First. You may even say. The signiﬁcance of this emphasis on the picture as it is used is not yet apparent. From the beginning. self-interpreting entity.11: “The picture presents (vorstellt)19 the states of affairs (Sachlage) in logical space.11). Wittgenstein goes on: “I could also use a measuring-rod as a symbol.18 This emphasis is made even more explicit by Wittgenstein in a later conversation about the Tractatus with Waismann. that is.20 Still.” From the start. The above passage would appear to suggest – and our later discussion will make clear – that the comparison is to be taken quite seriously. It is important to note at once the emphasis here on picturing as an activity: we make pictures of facts and to ourselves. taken as it stands. 2. Wittgenstein is viewing the picture not as an autonomous. and of nonexistent Sachverhalten are all closely linked. It is through the picture theory that we begin to see how this cluster of notions relates to the attempt to understand the unchanging substance at the heart of the world. We note. and therefore I might just as well have called propositions measuring-rods” (VC 185). of a “reality” that extends beyond the limits of the world.1). But we shall see how some such idea will be essential in making sense of the next several remarks. that it gives us the aspect of the picture that is crucial for Wittgenstein’s whole account. then. it would seem. it would seem. the world is understood always against a larger – logical – backdrop of what is not the case. for our own purposes.11 makes
35
.13: “The facts (Tatsachen) in logical space are the world. In many respects a proposition behaves just like a measuring-rod. insert a measuring-rod into a description and use it in the same way as a proposition. The reference here to “logical space” recalls 1. The move to a discussion of pictures is initiated abruptly. 2.1512 draw the analogy between a picture and a measuring rod (Masstab). without any explanation: “We make to ourselves pictures of facts” (TLP 2. After suggesting that the Tractatus’ notion of a picture was used to highlight certain important features of a proposition. that the Tractatus does in fact at 2.Pictures and logical atomism between facts.

For the temptation amongst commentators is to suggest. as 2. How could the picture considered in itself present a negative fact? Is what is not present in the picture imagined also to be part of what it presents? The elements of the picture stand for (vertreten. is a fact and it would seem to be just this “facticity” that allows it to portray. a kind of entity to which that picture must somehow be securely fastened. Wittgenstein’s emphasis on the facticity of the picture is in part meant to get at the confusion that would bring us to make such a
36
. however. a shadowy realm of all that is not but could be. indeed. but this seems to say nothing about the possibility of representing facts that do not exist. which. is just to reiterate the Fregean construal of the proposition (picture) as a kind of name (i.Wittgenstein’s Tractatus the problem of nonexistent facts seem yet more mysterious. Thus.22 To state the problem in this way. For on this conception we are naturally led to wonder what it is that can constitute the reference of pictures that depict facts that do not obtain.131).. Now clearly Wittgenstein is here implicitly challenging Frege’s assimilation of a proposition to a name. And. as analogues to the pictorial elements. as is often noted:21 propositions as pictorial facts must be sharply distinguished from names. It is to view the sense of the picture as something to which the picture corresponds. pictorial element).141 states. But it is essential to understand the real purpose of Wittgenstein’s attack on the Fregean conception. that the Tractatus is here ultimately concerned with the problem of how some particular picture fact can be connected with the appropriate world fact. It is then a short step – a step not actually taken by Frege himself. Black. It is 2. “go proxy for”) things (TLP 2. for example. we can now see how such a Fregean view is connected with the perplexity over the issue of negative facts. sees the picture theory as an attempt to give an account of how the relational proposition “aRb” could mean that some speciﬁc state of affairs cSd obtains. even while pointing out Wittgenstein’s difference with Frege. but one toyed with by Russell23 – to begin postulating a special domain of nonexistent facts.” The picture.15 that allows us to begin to understand the fundamental direction of Wittgenstein’s account: “That the elements of the picture are combined (verhalten) with one another in a deﬁnite way presents (vorstellt) that the things are so combined with one another. or at least that do not exist in the conﬁguration presented by the picture.e. serve only as proxies for objects.

To speak meaningfully of the picture as a “model of reality” (TLP 2. If a picture represents what-is-not-the-case in the aforementioned way. Wittgenstein states that it is just that these proxies for objects stand to each other in the way they do that says things in the world so stand. we might say.11: “The picture presents (vorstellt) the states of affairs (Sachlage) in logical space. The picture presents the existence and nonexistence of atomic facts precisely because it is the same picture that allows us to say that some fact either is or is not the case. as it were. For the picture says. it becomes apparent that talk of reference is completely beside the point. how it can express something about the world. but rather our having taken these proxies as a certain kind of fact about the world. Rather than leading us to imagine picturing as a relation between a new kind of entity – facts – we are urged to see that no real relation is at issue in the ﬁrst place. as it were: ‘This is how it
37
.” Wittgenstein is conceiving of the picture in relation to all those atomic facts it can be used to represent. For what we seek is not dependent on the existence or nonexistence of some entity. articulate. This is meant to bring out that what is doing the expressing cannot be the set of pictorial proxies as such. the picture. We could represent by means of negative facts just as much as by means of positive ones. these remarks from November 1914:
That two people are not ﬁghting can be represented by representing them as not ﬁghting and also by representing them as ﬁghting and saying that the picture shows how things are not. is in a certain sense an abstraction from the process of picturing. Compare. (NB 24) Negation refers to the ﬁnished sense of the negated proposition and not to its way of representing.” In speaking there of what the picture “presents. With this emphasis on the activity of picturing in place we can now better understand remark 2. the existence and nonexistence of atomic facts (Sachverhalten). (NB 23) In order for it to be possible for a negative atomic fact (Sachverhalt) to be given. This idea Wittgenstein indeed comes back to over and over again in the Notebooks. for example. but is instead part of what it means to have a picture in the ﬁrst place. But then if our concern is to explain how the picture is.12) thus presupposes understanding the picture within the context of its application. the picture of the positive atomic fact must be given.Pictures and logical atomism move. this only happens through its representing that which is not the case.

(NB 25)
The point would seem to be to emphasize the way in which the negative fact is dependent on. then. That is.) Positive and negative fact are coequal inhabitants of logical space. the Tractatus suggests that logic must properly inquire into the possibility of representation. In conceiving of matters in this manner we will be far less tempted to reify the negative fact. we see that our concern here must be to go. positive and negative fact stand on the same level. But that is to say that what is really at issue here is just the question of the nature of the fundamental categories in terms of which the world is constituted – for the Tractatus. a contrast between two uses of a picture.11. It is in the next several remarks that we see the core of Wittgenstein’s response. as it were. and to the question “How is it not?” just the positive proposition is the answer. or given entirely by means of. its positive counterpart.) At the same time. true or false. rather than attempting to explain how a particular picture can correctly designate some fact in the world. to account for the possibility of both together. (And here we should recall Wittgenstein’s initially suggesting that the negative fact lies in some sense outside the world. the question of the nature of substance itself. In recognizing the interdependence of positive and negative fact. we see that from the point of view of logic there is nothing sacrosanct about the existent fact either. of the particular deter38
. introduced together at 2. is how our propositions are capable of representing all and only states of affairs in the world. how it is that our propositions are guaranteed to make sense in the ﬁrst place. In the present context.063. in other words. behind these facts. the problem will have to do with giving some sort of speciﬁcation of the possibility of the picture’s “presenting” (in Wittgenstein’s special sense of this term)24 what it does. The effect of this whole discussion is then to bring into sharper focus the question which Wittgenstein believes is really at stake in this context. (This was the point of Wittgenstein’s identifying the total reality and the world at 2.Wittgenstein’s Tractatus
is not’. to attribute to it some special ontological status. What we want to explain ultimately. Now the possibility of the pictorial fact. The question that the picture theory begins to bring into relief is then the question Wittgenstein poses early on in the Notebooks: “What is the ground of our – certainly well founded – conﬁdence that we shall be able to express any sense we like in our two-dimensional script?” (NB 6).

qualities.131. the Tractatus calls the picture’s “pictorial form” (Form der Abbildung. indeed. TLP 2.” or even with the Kantian attempt to specify the fundamental categories that constitute the phenomenal world. color patches or what have you to stand for the objects composing that fact. the strategy of taking recourse in talk of an isomorphism is empty. The pictorial fact and the world fact that it represents would thus seem to operate within the same space of possibility.161 – the important question concerns his attitude toward this claim. rather.16 and 2.13 and 2.25 Wittgenstein’s answer to the question of how the picture – and hence language – can always be about the world is thus supposedly to be: they share a form.Pictures and logical atomism minate structure itself. is arbitrary: if my aim is to represent a book lying on a table. What is wanted. uses the term vertreten (“The
39
. and relations as the ultimate “simples. the choice of particular pictorial representatives. just as a way of expressing the absence of any such answer. Wittgenstein. In that regard. Still.15). why it is for Wittgenstein that we cannot at this level draw a meaningful distinction between the picture and what it depicts. And. One might usefully compare Wittgenstein’s approach here with the Russellian postulation of particulars. squares. it amounts to no more than the claim that depicting the world is possible because the world has the possibility of being depicted.1514 terms the picture’s “pictorial relationship” (die abbildende Beziehung). at 2. I insist that. The Tractatus’ assertion of the isomorphism between the picture and reality cannot be understood as an effort to offer the basis of an alternative answer to the ones provided by Russell and Kant but. it would seem. let us ﬁrst seek to become clearer on what it would mean to specify the picture’s pictorial form. while I certainly do not deny that Wittgenstein speaks of something in common between the picture and what is pictured – this is explicitly asserted at 2.131.26 Toward that end. is an account of the coordination of pictorial elements and objects referred to at 2. This then implies that our proper aim here must be to understand how we are driven into making this empty assertion. as an explanation of how the picture is always capable of depicting the world. the coordination that 2. just that this is the case is standardly taken to be the central contention of the picture theory. 2.151 states that this pictorial form is also the possibility of the things being related to each other in the same way. it is entirely up to me whether to use rectangles. Now clearly one dimension of this correlation.

later. it constitutes the ultimate ground of our ability to picture the world. the assuming of a particular outward appearance is not enough to guarantee that a set of correlated pictorial elements is a genuine picture in the Tractatus’ sense of the term. The legitimacy of the arbitrary correlations we set up would appear to depend in some sense on a deeper coordination of form. As the possibilities of combination common to the pictorial elements and the objects they stand for. (TLP 21512) 40
. for example. it is by means of the vertreten relation that what is earlier called the “content” of the object comes into view. (TLP 2.151 through 2.151) That is how a picture is attached to reality. name) and thing. the forms of the objects.1512:
The pictorial form is the possibility that the things are so combined with one another as are the elements of the picture.27 or picturing a situation in which red is louder than green? Evidently.Wittgenstein’s Tractatus elements of the picture stand [vertreten]. What is to stop me from.e. (TLP 2. that is. Wittgenstein’s way of attempting to drain this whole inquiry of its philosophical allure – the basis of his “solution” to the problem of the nature of substance – begins to become apparent when we closely consider remarks 2.29 The Form der Abbildung has to do just with this idea of a nonarbitrary. And that is to say that the speciﬁcation of the pictorial form would constitute a large step toward the fulﬁllment of one of the most fundamental tasks of philosophy. inner connection of the picture and reality.1511) It is laid against reality like a measure (ein Masstab – i. it then seems that we would come to see the essence of representation. for the objects”) to designate this connection between pictorial element (and. the a priori core both of our means of representing and of what is represented. in the picture. as traditionally conceived.. a ruler). it reaches right out to it. But setting up this sort of arbitrary correlation would not by itself seem sufﬁcient to ensure that any picture I construct will portray a possible state of affairs. placing a pictorial representative of an event into a pictorial representative of a hole. In laying bare the pictorial form.28 Only if the pictorial representatives have all the same possibilities of combination as their real world counterparts – only if they have the same form as those objects – will we say that they are really representatives of the latter.

a picture is seen to carry within it its inner coordinations with reality and thus cannot fail to depict. however. It is
41
. All that is necessary is for me to have a way of using the ruler. Conceived in this way.) For what Wittgenstein’s account is meant to bring out is that the essential possibilities of combination common to the pictorial elements and the objects are given. must always present some possible state of affairs. our hold on the picture is parasitic on a notion of the picture in use.30 The Tractatus similarly suggests that the possibility of depicting in general does not assume the existence of some fact or other in the world.171. Here. is that what makes something into a picture of the world – the pictorial elements being correlated with the things they stand for – is also what makes it into a picture in the ﬁrst place. And since.Pictures and logical atomism We must once more ask ourselves what it means to compare a picture with a ruler. This indeed is just what Wittgenstein suggests at 2. the pictorial form is parasitic on our way of picturing with a picture. after again stressing the importance of the picture-ruler comparison. of applying it to the world. is at the same time to suggest the insubstantiality of the pictorial form. as we have seen.” The point. normative status. the appearance of substantial necessity – in this case the necessity of the picture’s attachment to the world – is a mark of one’s failure to have made a genuine claim.1513: “According to this view the pictorial relationship which makes it a picture also belongs to the picture.31 To say that the inner coordinations with reality are part of the picture. (As always in the Tractatus. one of the pictorial forms referred to at 2. in other words. but only a way of picturing – a way of projecting our pictures. that method of projection can be said to be in a certain sense already given. A useful way of approaching this question is suggested by remarks 43 and 44 of the Philosophical Remarks. Wittgenstein’s point can be brought into sharper focus if we reﬂect on the notion of space.33 The above discussion is meant to get us to see the incoherence of supposing that in order to construct a spatial picture we must “have” beforehand a notion of space to function as a kind of constraint. Wittgenstein points out that the possibility of measuring in general does not presuppose a particular length for the object to be measured. It would then follow that a picture. precisely through the projection of the picture on to reality. once we are given the pictorial fact.32 Rather than having an a priori. simply in virtue of being a picture in the Tractatus’ sense. after the fact. as it were.

Wittgenstein’s Tractatus not. without the demand put forward in that question. we see that the show/say distinction functions as part of the attempt to dissipate the urge to look for any such “necessary features.172: “A picture. but also for their capacity to assume spatial relations. it is simply pointless to state as a general. but ineffable features of reality. But notice that. however. the possibility of introducing this language is dependent on the logician’s desire to get at the essence of representation. in other words. cannot depict its pictorial form: it shows it forth” (weist sie auf). Viewed in isolation. Instead. And that would seem to be just another way of stating the point of 2. the real point here is then to bring out the emptiness of the question motivating our whole inquiry. as if in constructing a picture of. a book lying on a table. self-standing claim either that something is or that something is not shown by this picture of a book lying on a table.” For it now becomes apparent that the assertion that the pictorial form can only be shown is equivalent to claiming that everything logic would want to say about the a priori nature of pictorial representation is a feature of how we operate with the picture. Instead. say. we see that the real aim of the Tractatus is to turn such an idea on its head. That is. With the above considerations in mind. but part of its way of being related to the world. however. to put it somewhat crudely.” The limits of my ability to make a picture of this kind then constitute the limits of my notion of spatiality – which is to say that this pictorial form is not a constituent of a given picture.
IV
The central Tractarian notion of showing is thus introduced at the crucial moment in the discussion of the picture. I must take care to have chosen proxies not only for these objects.
42
. this idea naturally leads us to imagine the existence of necessary. the idea that there is any contrast with “what can be said” has no role whatsoever. that these objects are in space – their spatial form – is revealed through my being able to construct a picture in the ﬁrst place: the fact that these two shapes can be correlated with that book and that table in such a way as to make a genuine picture gives us part of what we mean by “space. Rather than tantalizing us with the notion of an intrinsically inexpressible dimension to reality. his sense that there is. part of what this picture is.

35 Such an approach tends to treat that which is shown by the picture as a kind of unstateable presupposition of what the picture represents. Pears provides a good illustration of this view:
[Wittgenstein believed that] the possibility of saying some things in factual discourse depends on the actuality of other things which cannot be said. This implies. nonetheless has “actuality” as a kind of deep fact on which the possibility of depicting more superﬁcial facts ultimately “depends. at least in any sort of informative way.Pictures and logical atomism in this respect. we might say. But already we can see the way in which Pears’s reading assumes a quite substantial or robust conception of the “unsayable. a gap in our understanding of the world. but it does not include a diagram of that linkage.”38 The link between the picture and the world thus must seemingly defy all attempts at being fully represented. for Pears’s Wittgenstein.36
One’s immediate response here might be to wonder why a second picture could not be used to represent the linkage between the canvas and the sitter. Then the analogy with pictures was used to illustrate the dependence of the sayable on the unsayable: a portrait relies on the projective geometry which links the canvas to the sitter. a more general restriction on our language’s capacity to represent: the picture theory is ultimately construed as suggesting the impossibility of giving “a complete account of the sense of any factual sentence.34 The point in the present context can be made still clearer if we consider for a moment a more standard interpretation of the role of the show/say distinction in the picture theory. any such picture would ultimately have to “pick out the same facts about the sitter and use the same method of projection in order to pick them out. serves as a response to him. while this is of course possible.” To be sure. the show/say distinction. We now begin to see more concretely what we described in the Introduction as the fundamentally “dialectical” nature of the Tractatus’ argument – the way in which its central notions only have their life in relation to the philosophical temptations that the book aims to eradicate. Pears will construe the necessary inexpressibility of the pictorial form as part of the Tractatus’ attempt to
43
.”39 Now the question of just how the picture theory is to be extended to language in general we have yet to discuss.37 Pears’s answer is that.” The pictorial form. while somehow not capturable in any picture.

nor. constitute a very different sort of attack. is not to construe that form as a kind of full-bodied entity resting tantalizingly just beyond human reach. Wittgenstein could only show that we are incapable of adopting the sort of external vantage point from which a “complete” – and this presumably must mean nonredundant – depiction of the underlying.17). The temptation to which Pears succumbs is to suppose that the depicting relation – the relation between the picture and what it is in general directed toward40 – is here being treated as somehow undergirded by the pictorial form: the pictorial form constitutes a mysterious third element.Wittgenstein’s Tractatus place a limit on meaningful discourse. however. In this sense. On the Pears reading. ground of representation could be given. the picture theory would serve to present the logico-philosophical investigation into the ground of representation as fundamentally coherent. the pictorial form is no element at all. evidently quite real. but on the possibility of coherently imagining such a project in the ﬁrst place. a kind of metaphysical glue linking the picture and reality. nothing about the Pears’s construal of the picture theory suggests that there would be anything nonsensical about the attempt to give an articulation of pictorial form. indeed. but as in the end unsatisﬁable. in this case. This. Instead. Its purpose is served if we see that the inquiry in which we have thought ourselves to be engaged is predicated on
44
. the point only has force when we recognize in it the fundamental question of logic. But we have seen that the actual purpose of the picture theory is just to lead us away from such a view. The picture “must” have in common with reality its particular pictorial form precisely because this form is constituted by this picture’s application to the world – just as the possibilities of length are given through the ruler’s use in measuring magnitudes. But we must see that it would. to put forward any sort of “claim” that could coherently be challenged. stateable or unstateable. he might well agree with my claim that the show/say distinction forms the heart of Wittgenstein’s attack on the possibility of an inquiry into the essence of the world and its representation. Far from being imagined as a third element. The Tractatus holds that the picture “must have in common” with reality its pictorial form “in order to depict (abbilden) it – correctly or incorrectly – in the way that it does” (TLP 2. of course. but rather part of the picture’s way of depicting. At best. then. is that Wittgenstein’s real focus is not on the satisﬁability of logic’s project. My claim. After all.

the signiﬁcance of these notions must be explored. will appear within the context of a more explicitly “linguistic” discussion.Pictures and logical atomism imagining a kind of division between the essential possibilities of the world and the means by which these are represented. with the assertion of the inexpressibility of the pictorial form we have by no means exhausted the Tractatus’ discussion of the picture. It is to the latter issue that we shall turn in the next chapter. Moreover. we have yet to see exactly how the above account is meant to apply to the proposition. Still. how the initial points about the picture.
45
. as well those about the world and the nature of objects. truth and falsity. and the “representing” – as opposed to the “presenting” – dimension of the picture. To acknowledge that the pictorial form can only be shown is to acknowledge the incoherence of the attempt to draw such a division. logical picture. Wittgenstein goes on to introduce the notions of sense.

if Wittgenstein does in fact intend to distinguish the two. must have in common with reality in order to be able to depict (abbilden) it at all – rightly or falsely – is the logical form (die logische Form).182). but not every logical picture is spatial (or temporal or colored). we have seen.172 and 2. It is not at once clear. “Every picture is also a logical picture. is connected with the existence and nonexistence of atomic facts. On this account. then the picture is called a logical picture” (TLP 2.CHAPTER II
WHAT IS ANALYSIS?
I
Wittgenstein’s declaration of the inexpressibility of the pictorial form at 2. which is to say with everything that the picture can be used to depict. What is the purpose of holding that there is also common to the picture and reality another kind of form? The basis of Wittgenstein’s answer is suggested by the next two remarks: “If the pictorial form is the logical form. After all. the claim that the picture must share with the reality it depicts a pictorial form is central to the picture theory.181). the form of reality” (TLP 2. for example. not every picture is spatial.18).174 is followed by the introduction of a new notion – the logical form: “What every picture. The notion of reality.” we are of course called back to the discussion at the beginning of the picture theory. just how such an idea would differentiate the logical form from the pictorial.)” (TLP 2. With this mention of “reality. “Logical form” is thus to be understood as a more general term for the representational possibilities of any picture. (On the other hand. the logical form appears in some sense to contain the pictorial form: every spatial picture is to be construed as a logical picture. however. that is. But if this is
46
. of whatever form.

we will concern ourselves with the relation of picture and pictured only with regard to the bare possibility of their being logically linked.3 Thus. to serve as a means of shedding light on the signiﬁcant proposition. already begin to get a clearer idea of what is at stake in the introduction of the notion of logical form if we ﬁrst recall the ultimate purpose of the picture theory – namely. TLP 2. My suggestion. unclear. We can.1s. but also additional to the pictorial form – a feature of the picture on top of its Form der Abbildung?2 The precise nature of the generalization that Wittgenstein here alludes to would appear to be somewhat of a mystery. by generalizing the idea of form – by speaking not simply of what the picture must have in common with reality to depict it “in its particular way” (seine Art und Weise. however. To gain such an understanding will constitute the chief purpose of the present chapter. is that the notion of logical form is meant to ease this transition. as Friedlander seems to. that “logical form” describes something not only more general. And indeed. in reﬂecting on the thought or proposition as a “logical picture of the fact” (TLP 3). That is. “at the ﬁrst glance the proposition – say as it stands printed on paper – does not seem to be a picture of the reality of which it treats” (emphasis mine). although we might suppose the unclarity of this notion to be necessary. but also of what it shares with reality in order to depict it at all – Wittgenstein can hope to get us to think of picturing in cases in which no literal structural resemblance is involved. It then becomes apparent that Wittgenstein must somewhere address the obvious point that. say.17).011. despite the detailed consideration of the nature of representation in the 2. Now just how we are to conceive of such a “bare possibility” is. it seems we should call all pictures “logical” and speak only of logical form. it is not immediately evident exactly how the Tractatus’ remarks about the picture are to be extended to language in general. In fact. of how fundamentally this view diverges from that of Frege and Russell. then. of course. as he puts it at 4.1 Or are we to assume. following Dreben. a possibility that is presumably contained in the more tangible connection between. an adequate account of this generalization is in the end inseparable from an understanding of the Tractatus’ view of the nature and purpose of logical analysis. a spatial representation and the corresponding fact. is that. given the perspective the Tractatus
47
. the notion of pictorial form appears to become unnecessary.What is analysis? the case. in other words. The problem.

3.14 in phasizing the facticity of the propositional sign. by the time of the Philosophical Remarks Wittgenstein seems to doubt whether the generalization of the picture can in any way be legitimately employed:4
It’s easy to understand that a ruler is and must be in the same space as the object measured by it. is structured through our speciﬁc way of describing it. the reliance on the earlier points about the picture is quite explicit at 3. (PR 45)
Here the very possibility of the analogy between pictorial and logical form is called into question.1431: “The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables. just as was suggested in 2.? It sounds absurd. etc.Wittgenstein’s Tractatus ultimately aims to communicate.15 with regard to the difference between picture and pictorial element. The importance of this point will become apparent as we seek to elaborate the Tractatus’ development of the idea of logical form.
II
Many of Wittgenstein’s remarks about the proposition in the early 3s in fact closely parallel those about the picture.
48
. logical picturing would seem to be approached with an eye to such application. Nonetheless. The mutual spatial position of these things then expresses the sense of the proposition. or in the same space as a color. Indeed.14 – “What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another” – mirrors 2. in referring to the propositional sign as “articulate” and as other than a mere “blend of words. For in relying on the metaphor of the ruler. even in this criticism we see what Wittgenstein implicitly regards as central in the Tractatus’ extension of the notion of picturing. then. chairs.” In reﬂecting on the way the elements of a spatial picture are related to each other. But in what sense are words in the same space as an object whose length is described in words.141. As in the account of the ordinary picture.” brings to the fore the distinction between a fact and a name. with an eye to how “reality” in the Tractarian sense of the term. 3. he is once more bringing to the fore the application of a particular method of representation. Thus. books) instead of written signs. it would seem that we are meant to understand the essence of the proposition.

one way or the other. he is quoted as saying: “ ‘Objects’ also include relations: a proposition is not two things connected by a relation.1431 asks us to reﬂect on the spatial relationships between tables. The objects hang as it were in a chain” (CL 120). One obvious problem for this whole line of interpretation is that. we need not conclude from this that 3. The thrust of 3. constituents of the propositional fact. the argument goes. in a previously cited remark in the Notebooks. in the proposition expressing such a fact it is the relation of the letter “a” representing the book to the letter “b” representing the table that expresses the fact that aRb. with the question of the nature of Russellian relations misses the point. 3. are to be regarded as in some sense unreal. properties) are not objects and. Similarly.6 Rather.What is analysis? Now certain details of the Tractatus’ view of the notion of sense will have to await treatment in the next chapter. instead.1432: “We must not say.1432 is then to claim that relations (and. books. in a conversation about the Tractatus in 1930– 31. ‘Thing’ and ‘relation’ are on the same level. ‘That “a” stands in a certain relation (einer gewissen Beziehung) to “b” says that aRb’. But already we are in a position to approach the controversial and much discussed remark 3.
49
. ‘The complex sign “aRb” says “a stands in relation R to b”’. but we must say. the spatial relationship between the table and the book is not itself part of the picture. it is maintained. For. what it tries to represent is instead shown by “a” and “b” bearing to each other a certain relation. contrary to Russell. Wittgenstein appears explicitly to deny this claim: “Relations and properties. in a picture depicting a book lying on a table. thus. I suggest that the whole attempt to view this remark as centrally concerned. can we automatically assume that the Tractatus’ notation is to be assimilated to Russell’s – that Wittgenstein holds the “R” in “aRb” to represent the sort of thing designated by “is lying on” in a sentence like “The book is lying on the table”? Close consideration of this remark in conjunction with its predecessor would seem to suggest. in this context at least. but. Still.1432 is therefore an attempt to establish that relations and properties are. indeed.” This remark is often held to suggest something about Wittgenstein’s view of the unreality of properties and relations. etc. too” (NB 61). and so on in a propositional sign composed of these elements. “R” thus does not name anything. are objects.5 Thus. In the same way. is shown by the fact that these objects are related to each other in the way they are. after all. that this is not the case. by extension.

of the picture’s sense: we are to see it is just that the pictorial elements stand to each other in the particular way they do that allows the picture-proposition to be expressive. in general. consists in a particular arrangement of pictorial elements against the background of space. Nothing further is involved – only the taking of these pictorial elements as a fact within space. one seems to conceive of the proposition as essentially made up of a number of distinct elements that stand in need of uniﬁcation. to depict some deﬁnite arrangement of objects in the world. if we take a book lying on a table as a depiction of a pencil lying on a chair.15. We can then ask: how are we now to understand.15. therefore. which represents Wittgenstein’s actual concern here.182 makes clear). we are involved in generalizing in a certain way the earlier remarks about the picture. and other so-called material relations. We “must not say” that the complex sign “aRb” says “a stands in relation R to b. as we have suggested. It would seem. in moving to an explicit account of the proposition.Wittgenstein’s Tractatus It is these mutual spatial relationships that are said to “express the sense” of the proposition.8 His response will then be seen to parallel – and provide a further elaboration of – his remarks about the structure of the picture at 2. Thus we become tempted to posit the existence of something like a “logical form” to hold together the propositional elements.142. So. the question of the general nature of the propositional unity. just this question. not the issue of the reality or unreality of spatial. I suggest. the proposition? It is. the expressiveness or sense of the logical picture should be understood against the backdrop of the logical form. since not all pictures are spatial (as 2. temporal. as in 2.7 Instead. we can say. this sense. to see it as the key to the explanation of the proposition’s ability to have a sense. as in Rus50
. the connection amongst the elements of the logical picture. it is the book’s position vis-a-vis ` the table that would express the sense of this picture-proposition. that as the expressiveness of the spatial picture takes place against the backdrop of a spatial form. The point. But it cannot always be literal physical space – or not this alone – that constitutes the background against which the elements in an arbitrary propositional sign aRb are able to depict. is thus to bring out the self-sufﬁciency.” because to do so would lead us toward a confused understanding of the expressive power of the proposition. as it were. We are then naturally brought to focus on the apparent special relation reﬂected in the propositional sign. For in putting matters in this way.

To say along with the Tractatus “That ‘a’ stands in a certain relation to ‘b’ says that aRb. we are acknowledging the intimate connection between being a proposition and having a sense. is then merely an internal feature of our notation. the function sign is able to combine with a name because functions have some special connection with objects puts the cart before the horse.1432: “States of affairs (Sachlagen) can be described but not named. Similarly.What is analysis? sell’s multiple relation theory. It is to see that the claim that. Notice.144). is nothing other than the particular arrangement of propositional elements against the backdrop of logical space. as when we write “f(a).
51
. In seeing the proposition as akin to an arrow. An arrow does not connect to the direction it speciﬁes by means of some intermediary. we are acknowledging. rather. for example. (Names resemble points.” is not to replace one account of the nature of the propositional unity with another. Wittgenstein’s point.9 or to speak. we might say. it is the speciﬁcation of a direction. on this view. an outgrowth of the way we have decided to preserve the propositional unity in our analysis. as Frege does.” All of this is summed up for Wittgenstein by saying that a proposition must be distinguished from a name. it is only because these constituents do combine to yield a signiﬁcant proposition that we are able to draw the distinction between functions and objects in the ﬁrst place. propositions resemble arrows. as he maintains in the remark following 3.” We can thus say no more of the unity characterizing the signiﬁcant proposition than that it consists in the particular way these elements hang together in the propositional sign. something that must be added to the proposition in order for it to be capable of expressing that fact. but is instead constituitive of it: sensicality. by contrast.11 The relation R. the sense of the proposition – its “direction” – cannot be viewed as external to the proposition’s nature. then. is that our entire hold on the supposed relation between a and b in the assertion that aRb is parasitic on how we are able to operate with “a” and “b. instead. To suppose that a Sachlage could be named is inevitably to be led into searching for some further element. they have sense)” (TLP 3. but rather to give up the whole attempt to inquire into such a question.10 Wittgenstein seeks to eliminate these temptations at their root. it corresponds to what might also be expressed in the use of different signs for functions and objects. of the inherent “unsaturatedness” of the function as making possible its combining with an object in the judgment.

’ The simple signs employed in propositions are called names” (TLP 3. The key to making sense of the Tractatus’ position in this regard lies in a close consideration of 3.202). but is instead a necessary consequence of his whole conception of logical analysis.”12 Still. and this will either be right or wrong.
III
The Tractatus’ account of the name is bound up with the idea of a complete analysis of the proposition: “In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.13 Let us now quote this remark in its entirety:
A proposition about a complex stands in internal relation to the proposition about its constituent part. A complex can only be given by its description.24. The proposition in which there is mention of a complex. That this omission is no mere accident on his part. That a propositional element signiﬁes a complex can be seen from an 52
. Through a consideration of this issue. These elements I call ‘simple signs’ (einfache Zeichen) and the proposition ‘completely analyzed. if this does not exist. a remark that we began to discuss in the previous chapter. we may grant that it will be nonsense as far as Wittgenstein is concerned to give an example of a completely analyzed proposition. Wittgenstein notoriously never offers an example. And as that earlier account centered around the essential or nonarbitrary dimension of the pictorial element. becomes not nonsense but simply false.Wittgenstein’s Tractatus however. should be evident from 5. one has always concerned what an actual analysis into elementary propositions consisting only of names might look like. that this whole account quite naturally opens up the question of the nature of this supposed “backdrop.5571 alone: “If I cannot give elementary propositions a priori then it must be obvious nonsense to try to give them.” the possibility of the proposition. just as Wittgenstein’s discussion of the pictorial fact was seen to clear a space for an inquiry into the nature of the pictorial form. Thus. while still inquiring into why the possibility of such an analysis is thought to be so important. so here his inquiry turns to the nature of the logical form. Among the many mysteries that the Tractatus presents.2–3. we can gain an understanding of the Tractatus’ view of the name and the nature of logical form. so at this point he is concerned to investigate what is essential in the name.

Wittgenstein points out that this is just to say that whatever corresponds to the nonsimple propositional element is. to make contact with the simple objects corresponding to the genuine names. 8). on logic to tell us what we really mean. In the ﬁrst instance. But Wittgenstein explicitly disavows this conception in the Notebooks: “This is surely clear: the propositions which are the only ones
53
. we suggested that part of Wittgenstein’s concern here is to bring out the misleading nature of the notion of the complex. but is rather made manifest through another proposition. as we saw. If our intuitive understanding of “complex” is of a term designating an entity having constituents or parts of some sort – and it is difﬁcult to imagine what other sense could be given to this notion – then it would seem that any analysis of a proposition making mention of a complex would proceed by way of a further description. It now becomes clear that the components of the unanalyzed proposition should not be construed as names. then.144 between the name and the proposition. this account leads us to wonder about how ordinary language manages to function. reﬂection on the notion of analysis helps to make sharp the distinction just drawn at 3. The combination of the symbols of a complex in a simple symbol can be expressed by a deﬁnition. an object.What is analysis?
indeterminateness in the propositions in which it occurs.
In our earlier discussion of this passage. that we therefore have to wait on analysis. p. It may seem as if Wittgenstein is committing himself to the claim that the sense of the unanalyzed proposition is somehow undetermined. But. structure is represented only by structure. as has been stressed in the picture theory. (The notation for generality contains a prototype). We know that everything is not yet determined by this proposition. though. not a genuine component of the world. or series of propositions. suggesting in the Introduction that the Tractatus is concerned to lay down “conditions for a logically perfect language” and that ordinary language only has meaning “in proportion as it approaches to the ideal language which we postulate” (TLP. At the same time. Is such a view not implied in the above assertion that the appearance of the complex is marked by an “indeterminateness” in the proposition? Certainly Russell reads Wittgenstein in this way. simply by virtue of their superﬁcial appearance as the designators of entities. from the point of view of logic. Its complexity is not named.

This whole enterprise would thus seem to depend on the original proposition already having what Wittgenstein at 3.251 calls a “determinate” (Bestimmte) sense. a paraphrase of at least some aspect of the unanalyzed.. then it must be portrayed in the proposition to the extent that it does determine the sense. e. and mean something complex by that and nothing depends upon the way it is compounded. the way in which analysis could not be possible unless this were the case. a certain “indeterminateness” in the nonelementary proposition then serves as a means of allowing for the possibility of its analysis – which is to say for the possibility of the deﬁniteness of its sense.” we must recognize that his suggested analysis can have a hope of admissibility only if we are willing to regard the analyzed expression – “ ∃y (By & ∀x (Px ↔ x y))” – as. On this account. in Quinean language. then a generalization will make its appearance in the 54
. But Wittgenstein’s point becomes clearer when we understand the important claim in the above passage that we know that everything has not been determined by the unanalyzed proposition. given that Wittgenstein here and at 4.14 And. indeed.e. . For if I am talking about.23 and 3. To illustrate. The suggestion here would seem to be that the undeniable vagueness we ﬁnd in the nonelementary proposition is in a certain sense circumscribed: just because I can take into account the way in which my expression is imprecise it is able to function perfectly adequately in ordinary contexts. . let us consider Russell’s way of handling nondenoting concepts in his Theory of Descriptions (an important example. this same idea is expressed in the above passage from the Tractatus. For in saying that the proposition about the constituent (i.0031 seems to regard it as the paradigm of analysis).. Whatever we are to say about the correctness of Russell’s treatment of sentences like “The present king of France is not bald. Wittgenstein would seem to be calling attention to the way in which logical analysis demands the preservation of sense. .Wittgenstein’s Tractatus that humanity uses will have a sense just as they are and don’t wait upon a future analysis to acquire a sense” (NB 62). Wittgenstein elaborates this further in the Notebooks:
If the complexity of an object is deﬁnitive of the sense of the proposition. the analyzing proposition) is “internally” related to the proposition about the complex.g. This idea may seem to have an aura of paradox about it. this watch.

e.. is intrinsic to a generalization. from Wittgenstein’s perspective. but it is an indifferent matter. in that awareness of the referent’s composition is necessary for fully understanding what I mean. 2. “the watch” plays the part of an arbitrary member of what Wittgenstein will call a series of forms. Central to the Tractatus is the thought that sensicality must be conceived as independent of the way things happen to stand (see. to a full speciﬁcation of its components. one can easily believe that true and false are two relations between signs and things signiﬁed with equal rights. But this is not to say that I must conduct a complete investigation into the physical makeup of the watch before I can speak meaningfully about it. e.
Let us suppose that I assert that a watch is lying on the table and wish to infer from this that a wheel inside the watch is also lying on the table. The role of analysis. indeed made possible by. My claim about the watch then makes room for that (apparent) object’s complexity without committing itself.What is analysis?
proposition and the fundamental forms of the generalization will be completely determinate so far as they are given at all (NB 63–4). We can now see why both 3. as to precisely where.24. is to specify in some manner the particular members of that series. We know that the features of the object fall within a speciﬁed range of possibilities. TLP 4.”). the previously discussed counterpart to 3.. as it were. “The watch” here can be said to refer to something complex. For the indeterminateness that marks the appearance of a complex is just the arbitrariness that. to individuate that which is indicated in the unanalyzed proposition only en masse (i. as far as this proposition is concerned. it is enough for the sense of this proposition for me to know of the thing lying on the table simply that there is some mechanism inside of it. a certain indeﬁniteness in our ordinary propositions. as the close of 3. but the key idea is that “the watch” in the above nonelementary proposition is being treated in effect as a variable. describes the process as follows: “Every statement
55
.0201. Deﬁniteness of sense would thus appear to be compatible with. The details of his view of generality will have to await our discussion of the quantiﬁer in the next chapter. it would then seem.061: “If one does not observe that propositions have a sense independent of the facts. as a combination of symbols linked to a simple symbol only via deﬁnition).24 and the Notebooks passage above speak of generality in connection with the nonelementary proposition.g.24 suggests.

quite opaque.” The analysis would then be concluded – the statement about the complex would be resolved into those propositions in which that complex is “completely described” – when we have produced a series of sentences in which the quantiﬁer no longer appears. of course.Wittgenstein’s Tractatus about complexes can be analyzed (zerlegen) into a statement about their constituent parts. that an analysis of this nature must ultimately involve a kind of empirical investigation. on the basis of this account. if the watch in the above example could be completely characterized in terms of a description of the color (C) and shape (S) of its parts.16 then the analysis of the proposition asserting that the watch is lying on the table – assuming that the phrase “lying on the table” (L) could be understood as indicating a form – would begin with an existentially quantiﬁed statement of the form: “∃x(Cx&Sx&Lx).17 Still. given that I have not engaged in the appropriate investigation of the watch. For how would we determine what are the ultimate components of the watch (and hence what needed to be described by our analyzing propositions) without opening up that watch and literally taking apart piece by piece its internal mechanism? If Tractarian analysis indeed does entail such a process. Hence I cannot be supposed to really understand my assertion “The watch is lying on the table” – such an understanding could only be had by a watchmaker or perhaps a physicist. it begins to seem as if sense can’t be construed as independent of circumstances in the world. it may well seem. That is.15 we may suppose that the ﬁrst part of this claim is envisioning something along these Russellian lines. in an absolutely perspicuous form. and into those propositions which completely describe the complexes” (TLP 2. all the categories or forms that would be necessary to describe this structure. But given the above noted importance of Russell’s Theory of Descriptions to Wittgenstein’s conception of analysis.0201). This remark is. Thus. however. the sense that belongs to the propositions of ordinary language. even by Tractarian standards. And this is to say that analysis would then seem to be required to reveal the actual sense of the proposition – contrary to what we
56
. it would appear that I must remain ignorant of much that has in fact been left open by the unanalyzed proposition in which a representative for this object appears. After all. the “statement about [the] constituent parts” of the complex would involve a claim asserting the obtaining of a series of conditions – namely. Logical analysis can thus serve to present.

there is absolutely no need for it to FOLLOW LOGICALLY that a wheel which is in the watch is not in the drawer.21 A concept that does not have “sharp boundaries” in this sense is thought to be entirely meaningless. Is this not the view to which Wittgenstein is ultimately committed? The Notebooks makes it quite apparent that this is not the case: “If. there can be no question of my attempting to mean something of which I am completely unaware. better.20 Frege famously holds that a proper scientiﬁc concept is one that must be capable of deciding for every object in the universe.g. but rather to characterize that vagueness – or. to show that such vagueness poses no threat to the ability of the ordinary sentence to express.What is analysis? have suggested.19 Its purpose will not be to eliminate the vagueness of the unanalyzed proposition. If someone were to drive me into a corner in this way in order to shew that I did not know what I meant. e. whether or not it falls under that concept. not of some idealized or unattainable sense. Here he would seem implicitly to be moving against Frege and a Fregean approach to analysis. Thus Wittgenstein comments in the Notebooks that his whole concern could be described as one of “justify[ing] the vagueness of ordinary sentences” (NB 70. but if the watch were in such-and-such a position would you still say it was lying on the table?” And I should become uncertain. I mean just
57
. this is confusing a requirement for a more consistent application of signs – which indeed is important for genuine science – with a condition of their sense. Intrinsic to Wittgenstein’s approach. For Wittgenstein. he remarks several pages later: “It is clear that I know what I mean (meine) by the vague proposition” (NB 70).. it would seem. This shews that I did not know what I meant by “lying” in general. Similarly. is a distinction between the vagueness of a sentence and the determinateness of its sense. emphasis mine). for perhaps I had not the least knowledge that the wheel was in the watch.18 Tractarian analysis must instead always be understood as analysis of my sense. though. I say that this watch is not in the drawer. and hence could not have meant by ‘this watch’ the complex in which the wheel occurs” (NB 64–65). The point can be brought out through consideration of another passage in the Notebooks:
I tell someone “The watch is lying on the table” and now he says: “Yes. we might then say.22 For Wittgenstein. I should say: “I know what I mean.

Wittgenstein’s Tractatus
THIS,” pointing to the appropriate complex with my ﬁnger. And in this complex I do actually have the two objects in a relation. (NB 70)

It is here admitted that I will not ordinarily be prepared to say of all possible locations of the watch whether or not it can be said to be lying on the table. But why should this be taken to imply that I did not know what I meant in the ﬁrst place? It is not as if, in uttering my sentence, I am attempting to perform a scientiﬁc experiment and it is crucial to have something to say in every borderline case. Wittgenstein suggests instead that what is necessary for my proposition to have a determinate sense is only that it allows for some range of locations that will count as the watch’s lying on the table (and some range that will count as its not doing so); for there to be something that I mean in this instance the existence of a paradigm case is sufﬁcient. Surely, though, this condition is satisﬁed by the sentence about the watch, and, moreover, in its general formulation, by any sentence we should ordinarily count as meaningful. But then, on this account, all sense would turn out to be determinate sense – which is really to say that the notion of an intrinsic vagueness to what I mean must be seen as incoherent.23 We can now begin to see more clearly the idea behind Wittgenstein’s demand that analysis be ﬁnal or complete, as at 3.25: “There is one and only one complete analysis of the proposition.” For, as 3.23 suggests, such an analysis would seem to represent nothing but a way of expressing the determinateness that characterizes the sense of the proposition: “The postulate of the possibility of the simple signs is the postulate of the determinateness of sense” (emphasis mine). The point, in other words, is this. If I mean anything at all by my utterance, I should be able to render this in a perspicuous form, in the manner discussed above (that is, through a description of all the logically relevant features of the elements in my proposition). The question then arises as to whether such a speciﬁcation would be complete. To answer in the negative would seem to involve imagining that my assertion leaves something open intrinsically – as if I might later come to discover what I had originally meant. Witttgenstein’s assertion of the determinateness of sense is then really equivalent to (what we have seen to be) his dismissal of such a possibility as nonsense.24 Logical analysis must in principle always be completable. It is thus evident that the Tractatus’ principle of a complete analysis cannot be taken as a self-standing thesis about the nature of language
58

What is analysis? but, rather, is to be understood as a way of undermining the supposition of an essential indeterminacy in the sense of a sentence. At the same time, however, reﬂecting on this idea brings into sharper relief the proper aim of a philosophical inquiry. For what would it mean to give a complete analysis in the Tractarian sense? Analysis, as we have seen, is a process of laying out in a perspicuous form exactly what I mean in uttering some particular sentence. It is, we might therefore say, a matter of bringing to light the deﬁnitions implicit in the seemingly simple signs of the nonelementary proposition, since 3.261 (in a manner similar to 3.24) holds: “Every deﬁned sign signiﬁes via those signs by which it is deﬁned, and the deﬁnitions show the way” (TLP 3.261). This process of analysis will terminate when I have arrived at “primitive signs” (Urzeichen) that “cannot be analyzed further by any deﬁnition” (TLP 3.26) – that is to say when I have a sentence containing only genuine names. With the name we thus would appear to have a sign that can be given no further explanation of how it signiﬁes; it is in some sense in immediate contact with the world.25 In specifying the real names, it seems we are then making transparent the inner possibilities common to the world and the sentences that depict it, the logical core of reality. And that suggests that a complete analysis of the proposition will reveal nothing other than, on the one hand, the linguistic analogue to the pictorial form (the logical form), on the other, the timeless, unchanging substance described at the opening of the Tractatus. The conditions that must be satisﬁed for a speciﬁcation of substance can now be given more precise articulation: what is required is the identiﬁcation of the referents or meanings (Bedeutungen) of the names in the fully analyzed proposition. Such a speciﬁcation would, it seems, bring us almost literally to see the determinateness, the logical elements, that lie at the base of the signiﬁcant proposition. Wittgenstein implies something of this sort in this passage from the Prototractatus:
Although every word has meaning (bedeutet) via its deﬁnitions, this only means that these deﬁnitions are necessary in order to present in our sign-language the full linguistic depiction of the thought to whose expression the word contributes. But the deﬁnitions can be left tacit and the word does not then lose its meaning (seine Bedeutung), since it still stands in the same relation to the objects which are depicted by means of the deﬁnitions – only we do not speciﬁcally depict that relation. Naturally this often simpliﬁes the sign-language and makes the 59

Wittgenstein’s Tractatus
understanding of it more and more difﬁcult, because the decisive factor now lies outside the signs in something that is not expressed – their relation to their objects. (PT 3.202111)

A sharp contrast is here drawn between the purposes of logical analysis and those of ordinary human communication. While ordinary communication requires a certain simplicity of expression, logic seeks to articulate the full complexity of our language. Its aim in doing so is not to provide the elements of the proposition with a Bedeutung – as we have seen Wittgenstein’s fundamental thought is that logical analysis cannot serve to “improve” our language in this way – but, rather, to lay bare the relation of the sign to that Bedeutung. The question of how the realization of this “decisive factor” is achieved by analysis then becomes the question addressed by the 3.3s.

IV

Still, it is not at once apparent just why there is a question here. For if the Bedeutung is the object for which the name stands, as 3.203 appears to state, and I have analyzed the proposition into names, what more is there for me to say about that Bedeutung? If you ask me who is in the room, and I tell you John, Mary, and Ivan, surely that reply would count as sufﬁcient (even if it were incorrect). We might then suppose that Wittgenstein’s ultimate point about the unsatisﬁability of the logico-philosophical inquiry must depend on his later claim about the impossibility of specifying the elementary propositions a priori – as if that inquiry’s goal would be realizable but for an unfortunate restriction on human analytical capacities.26 But I suggest that this is not how his argument proceeds. Instead, the point of the upcoming remarks is precisely to see why the attempt to specify the Bedeutungen is unlike my above example of listing the individuals in a room by name. Wittgenstein’s aim here, in other words, is to bring to the fore the essential ambiguity of the notion of a “logical object” – the very notion that lies at the heart of the thought of Frege and Russell. Indeed, 3.3 has a distinctly Fregean ring to it, calling to mind his famous “context principle” from the Foundations of Arithmetic. “Only the proposition has sense; only in the context of a proposition has a name meaning” (TLP 3.3). We might suppose that Wittgenstein is here merely echoing what Ricketts has called Frege’s “judgment-centered
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again we must pay attention to the way these signs contribute to the sense of the propositions in which they occur. at 3. on the face of it. nothing but the sign in its “signiﬁcant use. “Every part of a proposition which characterizes its sense I call an expression (a symbol).) That. for example. It is. it is incoherent to suppose that they might occur in isolation. Wittgenstein repeats this point several times. although less obviously.326 suggests. however. An expression is any part of a proposition that contributes to the sense of the whole.” To grasp an expression will then entail the recognition of a “common characteristic mark of a class of propositions” (TLP 3. (The limiting case of this claim will be the one in which the expression is a proposition. Waismann. for example. one expression would be given by seeing what is common to the propositions “The cup is red.31). a Russellian propositional function “whose values are the propositions which contain the expression” (TLP 3313). the point is that an expression is constituted by the occurrence of some sign or signs within a certain set of propositions. which is.” Now it is important to emphasize here that the mere occurrence of the words “is red” does not by itself ensure that these sentences have something in common. Rather. Expressions are everything – essential for the sense of the proposition – that propositions can have in common with one another.” “The book is red.What is analysis? metaphysics. For what is the force of restricting the Bedeutung of the name to the propositional context? Wittgenstein’s answer is developed through the new notion of an expression (Ausdruck).” and so on – that is to say by the propositional function “x is red. Thus.”27 But while it is true that Wittgenstein is emphasizing the primacy of the judgment. and Carnap that in the sentences “The table is brown” and “The surface of the
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. his way of developing this idea will assume a very un-Fregean cast. (The proposition itself is an expression). Its appropriate presentation is by means of a variable in Wittgenstein’s sense.” “The table is red. An expression characterizes a form and a content” (TLP 3. as 3. We can then only identify expressions by reference to the propositions in which they occur. is not to suggest that an expression is some sort of free-ﬂoating object that propositionally bound signs can alone latch on to successfully. he suggests in a later conversation with Schlick.323: “In the proposition ‘Green is green’ – where the ﬁrst word is a proper name and the last an adjective – these words have not merely different meanings but they are different symbols [expressions].” Similarly.311).

while in the ﬁrst sentence “is heavy” can be meaningfully substituted for “is brown.Wittgenstein’s Tractatus table is brown” the phrase “is brown” constitutes two different expressions. however. Now we can begin to become clearer on the import of Wittgenstein’s “context principle. and that the name therefore stands for a meaning in the same way that a red patch might serve as a pictorial representative of a chair.” We might say that the variable is ultimately nothing but a certain way of regarding a sign or sequence of signs. the claim identifying all variables as propositional variables.28 An expression can be given only through a consideration of all the propositions in which some set of signs can occur. 3.314: “An expression only has meaning (Bedeutung) in a proposition. such cannot be his intent.”)” The natural inclination – one that is followed by most Tractarian commentators – is to suppose that Wittgenstein is here suggesting that “object” and “meaning” are simply interchangeable. by way of a variable. After all. The object is its meaning (Bedeutung). The proper presentation of an expression is.29 Wittgenstein’s context principle then serves essentially to equate this logical dimension of the sign with the Bedeutung of the expression.” which is restated in a somewhat different form at 3. This remark must instead be understood as a way of making evident what is meant by “the context” in which the Bedeutung of an expression is to be considered. it is the sign seen as logical mark of a class of propositions. or explained by.316: “What values the variable can assume is determined. as we have seen.314 is then emphasizing how the introduction of the variable requires our already being given a class of propositions. we can make sense of Wittgenstein’s way of introducing the notion of Bedeutung at 3. how the variable serves only as a kind of description of what those propositions share logically. (“A” is the same sign as “A. Every variable can be conceived as a propositional variable.” in the second this yields nonsense. This latter identiﬁcation may at ﬁrst seem surprising.203: “The name means (bedeutet) the object.” The context principle would seem to be somehow equivalent to. Clearly. The determinations of the values is the variable. We understand a meaning only when we look to how the propositional sign functions within a whole class of propositions. as if Wittgenstein were denying the possibility of the predicate calculus. But we saw earlier in our discussion of the picture theory that the Tractatus uses the term vertreten to designate this arbitrary relation
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. With this idea in mind. This indeed is stated more or less explicitly at 3.

It is to stress how grasping this nonarbitrary dimension of the name entails considering its occurrence in a whole class of propositions that Wittgenstein adds the parenthetical remark about “A” being the same sign as “A. in specifying those meanings we will have speciﬁed the fundamental categories of thought or language – that is to say. we see that two dimensions of the relation between signs and reality are distinguished – and. moreover. if the attempt to identify our basic logical categories is really another way of getting at the fundamental connection between language and the world. that the bedeuten relation has to do not with the arbitrary aspect of the relation between a sign and its referent. then. that two dimensions of the objects thereby depicted also emerge. given what we have said about the latter notion in the previous chapter. with what Wittgenstein would call an “essential” feature – namely. It now becomes clearer why the identiﬁcation of the Bedeutung will be of central importance in the Tractatus and. the way the sign contributes to the sense of the proposition in which it occurs. then Wittgenstein would be showing
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. but the object considered only with respect to its form. rather. (Note how 3. then. then. The endeavor to make evident such categories would seem to be what Russell has in mind in the Principles of Mathematics when he speaks of the need for gaining a clear grasp of the “indeﬁnables.) What the name “means” is thus indeed the object.”32 In Frege’s thought.” a task he presents as “the chief part of philosophical logic. the unchanging substance that is somehow at the heart of both.”31 Just as in the ﬁrst part of the picture theory. the concern with the fundamental logical categories is central. correspondingly.31’s reference to an expression characterizing a “form and content” echoes 2.22: “In the proposition the name is the representative of (vertritt) an object. how such a task is tied in to the Fregean and Russellian projects. For if the meanings of the names are equated with the forms of objects.” It appears.What is analysis? between a pictorial element and an object. That is. then.025’s similar claim about substance. the logical forms. expressing itself in his distinction between functions and objects. just as in our discussion of the text’s opening remarks.30 And indeed this same term appears again at 3. But. too. given the connection between a speciﬁcation of the meanings of the primitive signs and the more grandly metaphysical aims inherent in the remarks of the 1s and 2s. but. it would seem that Wittgenstein is here bringing out the truly exalted nature of the Fregean and Russellian projects.

Russell’s attempt to avoid the class paradox – the contradiction that ensues from assuming the class of all classes that do not contain themselves as members – and its analogues. And. we have already seen in our discussion of the ﬁrst part of the picture theory that Wittgenstein’s “completion” of (what he takes to be) the Frege/Russell project will entail a complete shift in our understanding of its nature. Of course. then propositional functions that apply to propositional functions that apply to individuals. Nonetheless. one in which no mention is made of the referents of the signs. of course. it is not at once obvious just what sort of “error” Russell is thought to have committed. just such a shift begins to become evident in this context in the remarks concerning Russell’s theory of types. In essence. The Tractatus could then rightly be said to be completing that work. it must admit of being established without mention being thereby made of the meaning of a sign. even without an understanding of the role of the term Bedeutung in the Tractatus.33 Certainly. it involves supposing a hierarchy of logical types of entities: at the bottom level individuals. bringing it to its inevitable conclusion. The theory of types is. is simply a
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. it ought to presuppose only the description of the expressions” (TLP 3. Many commentators suppose that Wittgenstein’s criticism is made in light of a proposed technical alternative to the theory of types. The theory of types serves to restrict the application of the propositional function only to entities of the immediately preceding level and thereby allows us to avoid the paradoxes. indeed. and so on.Wittgenstein’s Tractatus that the work of these authors has even greater import than they might have imagined. then (according to the presentation in Principia Mathematica) propositional functions that apply to individuals. Russell’s error is shown by the fact that in drawing up his symbolic rules he has to speak about the meaning of the signs” (TLP 3. Still. while the above remark makes it clear that the Tractatus regards this approach as somehow illegitimate.331). it should be evident from the reference here to the primacy of “description” of expressions that this passage. purely syntactical approach to logic:34 “In logical syntax the meaning (Bedeutung) of a sign ought never to play a role. the allusion to “logical syntax” could well seem to support the view of the Tractatus as arguing for a Hilbert-style. rather than constituting some new departure on Wittgenstein’s part.33). “From this observation [about the nature of logical syntax] we get a further view – into Russell’s Theory of Types.

Now. to hold that this move is an error is not to seek to impose some restriction on what such a theory can meaningfully express – a meta-theory of types as it were. by drawing the distinctions between individuals and propositional functions and between the different levels of propositional functions. as we shall see.35 Instead. One might then take a sentence like “The book is red” as characterizing an expression (recall from 3.What is analysis? continuation of the above discussion of the variable. we have just seen that to arrive at the Bedeutung of an expression one must consider a whole class of propositions with regard to what they have in common and determine how that common element contributes to the sense of these propositions. Such reﬂection. then. we are supposed to recognize that the referent of a name couldn’t be what we are looking for as the endpoint of our inquiry. it must be understood as part of the attempt to complete the kind of analysis spoken of in the Tractatus – that is. what Wittgenstein is trying to bring out is how this involves a misconstrual of what it would mean to complete the task of analysis. he has speciﬁed the logical forms underlying all thought and language.31 that the proposition itself is an expression). And that suggests that we should not view his talk of “logical syntax” as part of an attempt to advocate some particular technical approach to the study of logic. any more than we can suppose him to have provided speciﬁc guidelines as to how to carry out a complete analysis. but rather a fundamental confusion at its heart.” Wittgenstein is really saying that the theory of types is committed to treating the logical forms as if they might be named – that is. of the idea of analysis more generally. as an effort to set forth the fundamental logical categories. but only when some subset of these signs is
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. is meant to reveal not a slight defect in the Russellian approach to logic. it would seem that Wittgenstein is here and throughout concerned only to get us to reﬂect on the idea of analysis. that the real nature of the Tractatus’ criticism of Russell becomes clear when we view it in light of the above discussion of the context principle. as if they constituted further constituents of the fact that could be speciﬁed in advance.37 Rather. on how in general an analysis is to be carried out. Russell is seen as claiming that. In then suggesting that Russell must “speak about the meaning of the signs.36 For what is the theory of types ultimately seeking to accomplish? From Wittgenstein’s perspective. After all. I suggest.

This is what is suggested in 3. there is no paradox with which to concern ourselves. for the inner has the form φ(fx). φµ Fµ.333:
A function cannot be its own argument. is that the function (i. in a sense. while the second ranges over functions of type n 1. the meaning of “F” will then be determined by the use of certain signs common to that class.” Herewith Russell’s paradox vanishes. the ﬁrst “F” ranges over propositional functions of type n. if instead of “F(F(µ))” we write “(∃φ) : F(φµ). But then that is to say that it will be impossible
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.Wittgenstein’s Tractatus viewed in terms of its role in a particular class of propositions does it give us a meaning. he seems to be imagining that our grasp on the signiﬁcant sentence comes by way of a prior hold on the form. to use Russellian terminology. To believe that we could say that. though. Indeed. for example. For Russell. for example..38 The idea. “F” here is a schematic rendering of a class of propositions of a particular form.” the ﬁrst “F” and the second will therefore not have the same meaning. from the Tractarian perspective. In “F(F(fx)).” which by itself signiﬁes nothing. it is almost the opposite. we suppose that the function F(fx) could be its own argument. since. If. already an indication of a fundamental confusion. With the theory of types. the outer the form (φ(fx)). we recognize that. then there would be a proposition “F(F (fx))” and in this the outer function F and the inner function F must have different meanings (Bedeutungen).e. because the functional sign already contains the prototype of its own argument and it cannot contain itself. For Wittgenstein. we might say that Russell’s belief that there is even a need for a theory of types is. given the differences in the classes of propositions that they characterize. propositional functions ranging over individuals constitute one logical type would appear to involve supposing that it is this variable that dictates to the propositions constituting its domain – as if the logical form might represent a criterion of sense. the variable) is constituted entirely by the logical role it plays and these functions play different roles. Russell’s need to speak of what his signs mean bespeaks a tendency to attribute to logic just the wrong kind of priority. a form is determined only by viewing some string of signs as a logical mark. Common to both functions is only the letter “F.
Wittgenstein’s point is that when we become clear on what it means to treat a function sign as a variable rather than as a name. This is at once clear. Again. in other words.

that. Rather than seeking to “solve” “a paradox. require other dimensions as well. we still have to become clearer on the nature of the alternative being proposed by the Tractatus. as well as a position dimension. In this case. ‘The complex sign “aRb” says “a stands in relation R to b’ ”. we will be no more tempted to speak of “the class of all classes that are not self-members” than we would to ask about the weight of a noise. To recognize this is to acknowledge that a theory of types is unnecessary. of course. say. How will the meaning of a sign or set of signs be expressed in what Wittgenstein would consider an appropriately constructed language? From the above discussion. Rather. A thorough characterization of what I mean by “watch” and “lying on the table” will. of course.334). if we only know how every single sign signiﬁes” (TLP 3. This is. Let us then use as our example “The watch is lying on the table. but we must say. as we have seen. as the theory of types would suggest. the full enumeration of
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. a color dimension.39 Thus Wittgenstein adds at 3. With such an understanding. however.”): Wittgenstein’s aim is once more to bring out how our hold on a notion of logical form is parasitic on how we speak. ‘That “a” stands in a certain relation to “b” says that aRb’.
V
But if it is now more apparent why the theory of types is dismissed as misleading.334: “The rules of logical syntax must follow of themselves.What is analysis? to construct a (signiﬁcant) expression of the form F(F). where the two “Fs” constitute the same type of propositional function. it is certainly evident that such a language will not include any names for Bedeutungen.” In our analysis. it is just because the expression yields nonsense that we say these “F’s” are of the same type.1432 (“We must not say. because the two “Fs” in F(Fx) are of the same type that this expression yields nonsense. but Wittgenstein wants to show how this restriction is there expressed in a misleading way. we will be concerned to make perspicuous what is needed for this proposition to express its sense. For it is not. does not alone tell us how a Tractarian analysis of a proposition is to proceed. what will be required is. One is reminded here of 3. just the restriction that the theory of types is trying to institute.” our focus instead should be on gaining a clear understanding of the workings of our language. if by that we are imagining some a priori restriction on what is permissible logically. on what it makes sense to say.

if Wittgenstein is simply following and extending Frege’s insight. for example. Reﬂection on the notion of analysis thus makes evident how I might give a thorough description of the world without ever needing to have names of meanings.Wittgenstein’s Tractatus which will only be given with the completion of the analysis. Now what is central to notice here is that this speciﬁcation makes no mention of either position or color – the names in this language refer only to speciﬁc points within the coordinate system. these.and y-axes will be marked off in units of measurement. Still. simply checking off. are two of the meanings involved in the above sentence expressing its sense. For one might want to ask Frege just why his Begriffsschrift is supposed to be criterial with regard to the concept “horse” problem. The forms of color and spatial position are thus absorbed into my method of representation.41 and in a number of places in the Notebooks41): one set of x. the ordered pair 3. the appropriate points on my scale.40 Suppose. But suppose that color and spatial position are in fact among the dimensions. indeed. all Bedeutungen will similarly vanish into the particular system in terms of which reality is to be depicted.2 conjoined with an ordered pair representing a location on the color/ brightness scales. in other words.43 then the objection that we might bring against the latter also would seem applicable to the Tractatus. as it were. I will then express the claim that some position on the table has some particular shade of color as. further. another set of axes perhaps in units of color and brightness. they become part of the means by which I can describe the world rather than further elements that themselves have linguistic representatives. In the complete analysis of the above sentence. Why does the fact that the Fregean concept-script does not allow us to treat concepts as objects show that it is a “confusion” to attempt to make this equa68
. And. One is naturally reminded here of Frege’s aforementioned concept “horse” problem42 and his idea that the “ordinary language” distinction between concepts and objects will ultimately express itself only in the use of the signs of a canonical notation. as long as the scale of my coordinate system is well chosen initially I will be able to describe the color of any position on the surface of the table in the same manner. that I choose to express the analyzed sentence by means of a coordinate system (Wittgenstein in fact speaks of such a system at TLP 3. the forms that will be needed in the complete analysis. of logical forms.

For what reason are we to dismiss such talk as “nonsense”? These objections fail to take into account the dialectical nature of the Tractatus.44 For Wittgenstein. that they serve only to bring out the difference between Wittgenstein’s thought and Frege’s. then. color space only makes sense against the background of a particular coordinate system. Indeed. that coordinate system itself is deﬁned by the range of signiﬁcant “color propositions. in reﬂecting on the absorption of the logical forms into the particular coordinate systems that we set up. what we are meant to see is how everything we (as philosophers) would properly be looking for is built into the way we will speak. His whole position in the Tractatus (and in the later philosophy as well) rests on the assumption that we can make perfect sense with the language we already have: analysis.0411. 5. far from being committed to supposing that the analyzed sentence constitutes the “correct” form of expression.” “spatial position. or refrain from doing so – nothing whatsoever is here at stake. we seemingly have to speak of the logical forms in initially setting up the coordinate systems. one could seemingly ask Wittgenstein why the possibility of a certain kind of analysis demonstrates that Bedeutungen “really” cannot be named. And that is just to say that it must be nonsense to seek to specify the object of our search in advance (and remember that for Wittgenstein it is only in such an a priori manner that a logico-philosophical inquiry is to be conducted).475). then.” This becomes particularly evident when we reﬂect on how we would determine whether or not such a system is adequate. but that simply means that it allows us to express all and only what we want to express – that is. is in fact concerned to suggest the nonsensicality of such a notion. as we have suggested.” and so on. say. For although the speciﬁcation of some position in. Wittgenstein will later say that it is a matter of the set of signs having the right “logical/mathematical multiplicity” (see 4. that with
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. then..04–4. we might say. is discussed not in order to correct supposed deﬁciencies in our ability to speak and communicate. as Benno Kerry does? In the same way. we can in “colloquial language” speak of “color. but rather only for the purpose of making clear the nature of the logical investigation itself. As far as Wittgenstein is concerned. It is only if our aim is to identify the fundamental logical categories of our language (i.45 In this case.What is analysis? tion in ordinary language.e. then. if we are engaged in philosophy) that his distinctions between what can be spoken of and what cannot come into play.

Wittgenstein is to be regarded as again attempting to make evident the nature of the logico-philosophical inquiry itself.327: “The sign determines a logical form only together with its logicalsyntactical application. that. That which expresses itself in language. that it makes no sense to look for it. to be structured through the projection of the picture on to reality. but inexpressible features of reality. That which mirrors itself in language. so we see here a clear anticipation of 4. together with Wittgenstein’s subsequent insistence that that which “can be shown cannot be said” (TLP 4. is standardly taken as one of the clearest indications that the Tractatus is committed to the supposition of deep. For instead of ﬂatly asserting the existence of an ineffable domain of form. The propositions show the logical form of reality.” This remark.” It is. not by allowing us to “better understand” logical form (whatever that
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. however. or depicting an impossible state of affairs. the Bedeutung of an expression will emerge. For this notion of the emergence of the logical form through the proposition’s application mirrors precisely the way we have seen the pictorial form.121: “Propositions cannot represent the logical form: this mirrors itself in the propositions. the inner possibilities common to the picture and reality.47 Criterial in logical analysis is what we can meaningfully say and it is on this that we necessarily remain dependent. were either such eventuality to take place.1212). through the signiﬁcant use of the propositional sign alone that the logical form. They exhibit it.46 Notice.48 Wittgenstein’s whole point here is then really summed up at 3. A complete analysis into elementary propositions consisting only of names will make perspicuous how this is the case.49 This. brings us back to the central point of the picture theory. language cannot represent. in other words. And just as this latter idea led Wittgenstein to hold that the pictorial form can only be shown. To hold that logical form is only shown is to emphasize how the whole of the philosopher’s apparent subject matter is inextricably built into the coordinate system that allows us to express. in turn. we would reject this representational system (and not our ordinary standards of intelligibility) as inadequate.Wittgenstein’s Tractatus this system we never expect to end up either at a loss for words. But our discussion of the 3s should make plain how this interpretation of the show/ say distinction is no more appropriate here than in the context of the picture theory. we cannot express by language. as it were.

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. As Wittgenstein puts it:
We can. then. (TLP 3. nothing but to pay attention to the way the sign functions in the (signiﬁcant) sentences in which it ﬁgures. There is then in a sense nothing for us to do to specify a logical form. This of course does not preclude the attempt to develop a special notation. Wittgenstein’s claim that it is only the possibility of a particular symbolism that reveals something about the essence of the world is then meant to emphasize the emptiness of the attempt to specify that essence. It seems to go almost without saying that a logical inquiry can terminate only when it has seized on the correct formulation of its subject matter. the presumed canonical presentation of the logic of our language. This assumption ﬁnds expression in Frege’s very need to construct his Begriffsschrift. For if. for example. but by removing the temptation to imagine that there is anything to be understood in the ﬁrst place. spread out across a class of propositions: logic is not located at some single point in a system of signs. for example.What is analysis? would mean). when it has in some sense captured the object of its search.3441)
Certainly. (TLP 3. to use what is in this case Russellian notation for the truth functions. but is made manifest by the language as a whole. This point about the inherent unsatisﬁablility of the philosophical endeavor is further brought out at 3. can be replaced by the notations of “ p” (“not p”) and “pvq” (“p or q”). the logical dimension of the sign of any language only emerges in the way that sign is applied.3421:
A particular method of symbolizing may be unimportant. but the possibility of every single thing reveals something about the nature of the world. it is permissible.3421)
Here Wittgenstein is asking us to reﬂect on what it means to seek a logical or philosophical result. And this happens as a rule in philosophy: The single thing proves over and over again to be unimportant. as far as Wittgenstein is concerned. express what is common to all notations for the truth functions as follows: It is common to them that they all. so to speak. nor even deny that doing so might be helpful in certain ways. that aspect must be. (Herewith is indicated the way in which a special possible notation can give us general information). but it is always important that this is a possible method of symbolizing. as he has suggested.

This is just the thrust of 3. which signify an object. This in turn brings out more fully the inherent ambiguity of the notion at the center of the whole logico-philosophical inquiry. in any ordinary sense of the term but an internal feature of our own language. step by step. It would then follow. have in common. the
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.3411)
This notion of the “essential” in a symbol or expression is just another way of speaking of its Bedeutung. then. We must. which might be taken as the culmination of the discussion of the 3s. in other words.341 and 3. that the “speciﬁcation” can be no more than an acknowledgment that we speak.341 and 3. see these signs as characterizing an expression in the Tractarian sense of the term. it becomes apparent how the inquiry into the logical forms turns back on itself: what begins as an attempt to specify the necessary features of the world ends with the recognition that these extend as far as our language itself. (TLP 3. One could therefore say the real name is that which all symbols. that no sort of composition was essential for a name. sometimes nonsensically. that these signs stand on the same level as any other in the class that they serve to characterize. But then that is to suggest that the “real name” that logic seeks is ultimately no name at all: its “composition” disintegrates precisely because what it refers to is not a thing. sometimes with sense. In order to see the Russellian truth functional notation as revealing something of the “essence” of the world we must take these signs together with all other notations that can express the same sense. After drawing the distinction between accidental and essential features of the proposition. Again. Wittgenstein states:
The essential in a proposition is therefore that which is common to all propositions which can express the same sense. And in the same way in general the essential in a symbol is that which all symbols which can fulﬁll the same purpose have in common.Wittgenstein’s Tractatus But to say that this is a “possible notation” or that this constitutes a mode of expression which might “replace” other means of expressing the truth functions is to suggest that the notation does not give us by itself the inner logic of our language. But that makes evident that there is nothing logically privileged about the Russellian notation.3411. To hold that this essential aspect is arrived at by seeing what all symbols that can fulﬁll the same purpose have in common is thus really to reiterate how the logical form is spread out across a whole class of propositions.

Thus. the sky has deepened to become magenta. . however. That magenta is darker than sky blue is. we might say.What is analysis? notion of a logical object. to hold that they are pure ﬁctions. . to remove these “objects” from that relation is “unthinkable” just because we can have no independent handle on their identity. This section of the Tractatus intends to show precisely the fragility of such a perspective. built into the statements in which these
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.50 It is not that Wittgenstein wishes to ﬂatly deny the existence of such entities. His aim instead is to get us to see how their “existence” rests on the existence of objects as the arbitrary (or accidental) referents of names in the sensical proposition. it quickly becomes apparent how the distinction between formal concepts/properties/relations and proper concepts/properties/relations is really a kind of paraphrase of the points that have emerged in the passages we have been considering. Indeed. is one that “it is unthinkable that its object .122: “We can speak in a certain sense of formal properties of objects and atomic facts.
VI
Given this way of understanding the discussion of analysis in the 3s. stand in the internal relation of brighter and darker in that standing in that relation is constitutive of what they are. we might say that white should be added to that magenta paint if the latter is to approach sky blue or remark on how. a way of regarding the components of our genuine propositions. at sunset.” In what sense can we speak of such formal properties and relations? Wittgenstein makes clear in 4. for example. it would seem. it is the propositional constituent viewed in a special light. and in the same sense of formal relations and relations of structures. or of properties of the structures of facts. not possess” (TLP 4.1272 should come as no surprise. we (assuming we were ﬂuent speakers of English) would not remark on the magenta color of the sunset and then go on to wonder if the sky were darker than its ordinary color.123): two shades of blue. we ﬁnd ﬁrst at 4. Thus. The logical object is not a thing. An internal property. By contrast. but. Wittgenstein’s blunt characterization of the notion of an object as a “pseudo-concept” at 4.51 But then it would seem that we can “speak of” formal properties and relations only in the sense that we can utter propositions in which they ﬁgure as internal features.122 that the term “internal” can be substituted for “formal” in these contexts.

126)
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. as a further fact to be represented. But it is shown in the symbol for the object itself. the numerical sign that it signiﬁes a number. The sign that signiﬁes the characteristics of a formal concept is. The expression of a formal property is a feature (Zug) of certain symbols. it is thus as if we were imagining that a triangle formed from the intersection of three lines might somehow be viewed apart from these (mere contingent) borders. to assert a variable. perhaps. (TLP 4. In attempting to state a formal relation or property.Wittgenstein’s Tractatus words can meaningfully occur – which is to say that what we would want to express by this string of signs is shown by the existence of a certain class of propositions. Wittgenstein’s remarks about “formal concepts” express much the same point:
In the sense in which we speak of formal properties we can now speak also of formal concepts. An expression like “magenta is darker than sky blue” will be absent from the resulting class – will be nonsense – just because it attempts. whose values deﬁne the meaning of this notion. it supposes that what is common to a number of propositions exists alongside those propositions. the formal properties. we might say. This in fact is what Wittgenstein proceeds to assert about internal properties and relations generally: “The holding of such internal properties and relations cannot. to get us to see that everything we are really after here emerges simply through a description of the boundary lines that characterize this ﬁgure. are not expressed by the functions.) Formal concepts cannot. to use the terms of our above discussion. but it shows itself in the propositions which represent the facts and treat of the objects in question” (TLP 4. We can then say. therefore. a characterisic feature of all symbols. The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant. a number of propositional variables). etc. Wittgenstein’s purpose would then be to expose the incoherence of this fantasy of getting at the triangle itself.122). however. cannot be expressed by a proposition. For their characteristics. . whose meanings fall under the concept. That anything falls under a formal concept as an object belonging to it. be represented by a function. . . like proper concepts. be asserted by propositions. that the internal or formal features of a concept like “magenta” is properly presented by a propositional variable (or. (The name shows that it signiﬁes an object.

an expression of what these symbols have in common. . . But recall that the symbol (expression) is itself a way of characterizing a form. though. . that which is common to a class of propositions. rather than constituting some determinate position within that framework. the proper means of expressing a formal concept will then presumably be through what he calls a “formal series” – that is. there remains an essential difference between the propositional variable and its values.52 (For this reason Wittgenstein asserts at 4. Wherever the word “object” (“thing.) is rightly used. Wherever it is used otherwise. Thus. a whole system of symbols (such as the one characterizing the concept of being a successor) “ordered by internal relations” (TLP 4. we could say that a formal concept like “object” must be conceived as part of the coordinate system that allows us to express. cannot (meaningfully) be set down alongside the propositions that this concept ultimately serves to characterize. . there arise
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.1272.”. 4. Or. Wittgenstein says that such a concept is a feature of certain symbols – that is.” etc.What is analysis? We must ﬁrst notice the position that the formal concept occupies within the overall Tractarian framework.. i. as part of what some number of symbols are. Wittgenstein suggests that the formal concept. He can then be said to recognize in this sense no type distinctions with regard to variables: the formal concept is spoken of in exactly the same terms as the expressions it serves to characterize. to shift to the previous metaphor. presented by way of a propositional variable.1271: “Every variable is the sign of a formal concept. Nonetheless. as a proper concept word.”) By contrast. it is expressed in logical symbolism by the variable name. as if they all stood on the same level.e. It will then be nonsense to attempt to make assertions about such notions. In speaking of a formal concept Wittgenstein has thus ascended a level from his earlier talk of the proposititional variable. y) . just like an expression or symbol.” by “(∃x. For example in the proposition “there are two objects which . Wittgenstein suggests that a formal concept is. the ﬁrst bald assertion of the nonsensicality of the central notions of Russellian and Fregean logic53 – as well as those that the Tractatus itself has relied on – thus follows quite naturally from the previous remarks:
So the variable name “x” is the proper sign of the pseudo-concept object.1252).” “entity.

” “complex.Wittgenstein’s Tractatus
nonsensical (unsinnige) pseudo-propositions. who see the Tractatus as concerned solely to eliminate philosophical confusions.” “Number. say “There are objects” as one says “There are books. therefore.” “Function.” “fact. e. But in a more important sense. They all signify formal concepts and are presented in logical symbolism by variables.” “Fact. For we might well be inclined to ask: even if Wittgenstein has revealed “object” to be a formal and. For such questions reﬂect what we have seen to be a fundamental assumption (whether explicit or implicit) of many Tractarian interpreters – namely.” and all like them are nonsensical.” Nor “There are 100 objects” or “There are 0 objects. Still. if his ultimate aim really is to show the meaninglessness of all philosophical questions.” “there is only one number nought.” “function.
“Object. despite the preparation we have received for these claims. Even for those commentators who nominally reject this reading. not by functions or classes (as Frege and Russell thought).” The same holds of the words “Complex. So one cannot. After all. concept. that Wittgenstein is throughout the text attempting to provide arguments for controversial and disputable theses. ﬁnd further discussion of the notion of number in particular in the 6s and to that extent these questions are appropriate.” etc. they are apt to be experienced as too quick. to have a unique status. we then go on to protest. how has this been shown of these other central notions? Do we not require further arguments before this much more general conclusion can be properly drawn? We do.” “number. as it were.” and so on are all formal concepts in the above sense and consequently will not ﬁgure in any genuine propositions. laying his cards on the table when he comes out and says this (or something quite near to it). The temptation here is to imagine that “being a formal concept” is put forth as a criterion of nonsensicality. Expressions like “1 is a number. which has not yet been shown to
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.g. I would suggest that they miss the mark entirely.. he must be.54 But temptations only lead us astray in Wittgenstein’s austere world and so must be countered. of course. It is quite tempting to suppose that these sorts of utterances must occupy a special position in the framework of the Tractatus. mere pseudo-. the tendency is quite strong at these points to attribute to Wittgenstein something like a substantive doctrine. a criterion. (It is as nonsensical to say “there is only one 1” as it would be to say: 2 2 is at 3 o’clock equal to 4).

By contrast. emerging through reﬂection on the pictorial nature of the proposition and what it would mean to provide an analysis. We have sought to bring out that an understanding of the role of “object” in the Tractatus is its recognition as purely formal. That is. but we can come to recognize its precariousness: we see through the terms of the Tractatus. only formal? Our whole discussion thus far has been designed to suggest how this description is not adequate.” “fact. We do not thereby explain the philosophical perspective or reveal its true nature.” and so forth. as I have suggested above. But we must ask ourselves whether this as a criterion has been shown to “apply” even to the notion of an object. We might then say that the claim “It is nonsense to seek to represent an object” constitutes. This recognition. is that our notions of object.” “function.) The point. a purely grammatical remark.” “number. the Tractatus’ reﬂection on the nature of the proposition may lead us to understand differently the role of the object. is just the recognition of the nonsensicality (in the Tractatus’ sense of the term) of the attempt to provide a speciﬁcation of the object. of adopting a standpoint from which we can. formal concept. Rather than establishing the truth of certain propositions. moreover.” and so on.What is analysis? apply to “fact.” “number. (In Tractarian terms we could say that it is an expression of an internal relation. that the (philosophical) questions we were originally inclined to ask in connection with this notion have lost their allure. that the only philosophical hold we have on this notion is as an intrinsic feature of our way of representing the world. and philosophical nonsense are all given together. it may bring us to see. the task of the Tractatus at this juncture could then be described as one of characterizing the philosophical inquiry into objects so thoroughly that it crumbles under its own weight. once and for all.55 And that means that the insight into the status of one of the central Tractarian notions must be at the same time an insight into the rest. assess the “real character” of our utterances about objects. These terms. In acknowledging the weakness of our grasp on “object” we are acknowledging the same about “complex.
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. There can then be no question of offering criteria of nonsensicality. are all of a piece. is Wittgenstein’s method to make clear what an object is and then subsequently to go on to bring out how that concept is. to use the language of the later Wittgenstein. in other words. they are intended to characterize. however. a single viewpoint. after all. as I have claimed. in turn.

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. Indeed.” What the Tractatus seeks instead is to lead us to regard in a new way our attempts to gain clarity about all such notions. We are called to go on without philosophy. it would be nonsensical to attempt to do so a priori. thus expresses the comprehensiveness of the shift in outlook that the Tractatus aims to effect. since the logical forms are said to be “anumerical” (TLP 4.” “object.” and “number.” we might say. Rather. to go through all of our misleading notions one by one. we are meant to see that the same kind of move is described in the attempt to inquire into any of these notions. We do not by means of this text arrive at new. The “and so on. superior accounts of “fact. it seeks to get us to go on differently in our efforts to know the world. He plainly is not attempting to provide a complete inventory of formal concepts.128). that we are in every case involved in imagining an incoherent detachment from the fabric of our own language.Wittgenstein’s Tractatus This point becomes even more evident when we notice the phrase “and so on” that follows this list of central notions – the list as Wittgenstein gives it at 4.1272.

Would not the central steps toward ﬁnding “on all essential points. a third of the way through the Tractatus? What.4711 that this speciﬁcation represents the essence of the proposition and.471 and 5. we have seen that these remarks should be understood as more explicit statements of what is Wittgenstein’s fundamental point throughout – or. indeed. of the world. one might well wonder what work is left to be done after the 3s and early 4s. Instead. I have suggested that it aims to communicate
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. as indications of how we are to regard the seemingly more metaphysical claims in the earlier sections of the text. 4. perhaps better. then. that the account up to this juncture is in some sense only preliminary? We must recall once more the nature of the investigation in which the Tractatus is involved. It is not. and 4. Would such ideas not imply that the real focus of “logic” is yet to be expounded. however.CHAPTER III
THE ESSENCE OF THE PROPOSITION
I
Wittgenstein’s attempt to undermine what he sees as the heart of the philosophical endeavor would seem to be already well under way with the completion of his initial account of analysis.1274.54 denial of signiﬁcance to all of his own propositions – represent a sudden shift in the direction of the Tractatus. If we accept such an interpretation. one might also wonder how the account that we have given squares with Wittgenstein’s subsequent concern to specify the “general form of the proposition” and his claim at 5. that the straightforward attacks on the central notions of logic at 4.1272.128 – or even his later 6. is the purpose of the rest of the book? Moreover. the ﬁnal solution of the problems” (TLP Preface) of philosophy already have been taken. then.

Our central purpose. that indeed central to understanding the text (as well as the real character of its subsequent repudiation by Wittgenstein) is appreciating how it is committed to supposing a kind of essence to the perspective it expresses. it is one that evidently requires a good deal of structure to be maintained. in a sense. the Tractatus does continue. For Wittgenstein. (TLP 2. moreover. (TLP 2.202) 80
.
II
To set the stage for the discussion that we ﬁnd in these later sections of the book. in other words. and 6s add to that increasingly complex structure – the analysis of the logical constants. Nonetheless. it seems we should say that the Tractatus’ ultimate point can be grasped in its entirety at any juncture of the text. But this “making clear” must involve showing how these details can be regarded as part only of an extension of a perspective. we must ﬁrst return to the initial account of the picture.2 the identity of form between the picture and what it depicts. rather than the introduction of a fresh set of principles. Thus. 5s. is not in any obvious sense a mere repetition of the themes developed in the ﬁrst part of the text. The absence of any further work to be done at this stage is then not a criticism but rather just the point.” while at the same time preserving the sense of the whole endeavor as the expression of a single thought. the next several remarks all deal with a picture’s “representing” of a “possibility” of facts:
The picture depicts reality by representing (darstellt) a possibility of the existence and nonexistence of atomic facts.Wittgenstein’s Tractatus a single view of the nature of logic. If the Tractatus is to be seen as setting forth a single uniﬁed vision. then. as well as the introduction of various apparent technical moves. This continuation. there can be no “preliminary” stages for us to pass through. the speciﬁcation of the general form of the proposition. but instead involves a host of new terms and seemingly new questions. and so on. will be to elaborate Wittgenstein’s further working out of the “problems of philosophy.1 Our aim in this chapter is to make as clear as possible the features the 4s. the truth tables and the idea of logic as tautologous.201) The picture represents a possible state of affairs (Sachlage) in logical space. After reiterating at 2. no overwhelming need to go on once we appear to have grasped its central teaching.

the existence and nonexistence of atomic facts. What a picture represents would then seem to be the choice that is made among these facts laid out in logical space. Now I have already suggested2 that what a picture presents is all those states of affairs it can be used to depict.” It would seem that a picture “presents” existent and nonexistent atomic facts. Let us take the case of a picture depicting a book lying on a table.11: “The picture presents (vorstellt) the states of affairs in logical space. We then ask: what determines which one of these possible states of affairs is in fact represented by the picture in some given case? Wittgenstein develops his answer to this question at some length in the Notebooks. (NB 23)
The point in these passages seems to be that the possibility of a picture’s representing some particular state of affairs – and hence its capacity to be true or false – is dependent on the way that picture is as
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. a possibility drawn from the set. this picture will be said to “present” both the fact that the book is on the table and the fact that it is not on the table. but “represents” a possibility of such facts. in these passages from November 1914:
The picture has whatever relation to reality it does have. it is.201 – and 2.3 An example will help to make evident the signiﬁcance of this distinction between the presenting and representing dimensions of the picture. as it were.The essence of the proposition
The picture contains the possibility of the state of affairs it represents. (NB 23) The method of portrayal (Abbildungsmethode.4 The same picture will agree or fail to agree with reality according to how it is supposed to represent. (TLP 2. It “represents.03)
Note ﬁrst the parallel between these remarks – especially 2. as. a picture presents both existent and nonexistent facts because the same picture that allows us to say that some fact A is the case also allows us to say that A is not the case. method of depicting) must be completely determinate before we can compare reality with the proposition at all in order to see whether it is true or false. If we correlate the pictorial book with a real book and the pictorial table with a real table. The method of comparison must be given me before I can make the comparison. that is to say either the book’s lying on the table or it’s not doing so (but not both at once). And the point is how it is supposed to represent (darstellen).” by contrast.2. for example. some particular state of affairs in logical space.

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. Instead. would always introduce new elements – in co-ordination).Wittgenstein’s Tractatus a whole compared with reality: it is just our method of comparison that decides whether we understand this picture as holding the book to be on the table or not on the table. it is the method of comparison that determines whether a more complex picture depicting. It is important to see how. Wittgenstein then attempts to bring out the sense in which that “ﬁeld” is present in its entirety as soon as we have a picture of the world. as Wittgenstein puts it in the Notebooks. as if we were supposing that the negation of A includes. the possibility of applying any one of the logical constants might be said to presuppose the ability to apply all the rest. etc. as one might put it. with the help of the proposition denied. shows that what is denied is already a proposition and not merely the preliminary to a proposition. They are to be construed as the characteristic means of. the denial is already related to the logical place determined by the proposition that is denied. besides A. D and so forth. And. in the same way.0641:
One could say. is not some brute gesture toward the totality of things not identical with books on tables. according to this story. the so-called logical constants thus come to the fore. the denied picture carves out a distinct state of affairs. This whole idea is perhaps stated most clearly and succinctly at 4. states of affairs A and B represents A v B. at 3.42: “Although a proposition may only determine one place in logical space. With the focus on the representational capacities of the picture.” Part of the reason for this claim we have already alluded to in our brief discussion of negation. the whole logical space must already be given by it. occupying its own position in logical space. That negative fact. moreover. for example. The denying proposition determines a logical place. also B. A & B. the logical sum. (Otherwise denial. we are really saying that both facts are given together: if we know what it means for the book to be on the table we at the same time know what it is for it not to be on the table.5 For in pointing out that a picture of some fact A can be used to assert A. A B. say. The denying proposition determines a logical place other than does the proposition denied. C. That one can deny again the denied proposition. “project[ing] the picture of the elementary proposition on to reality” (NB 29). or any other truth functional combination. This is what he has in mind.. For the picture represents always a selection within the ﬁeld of what it presents. the logical product. by saying that it lies outside the latter place.

” etc. we should not be misled by this into supposing that “ p” speciﬁes a unique way of comparing the proposition with reality. then enable us to assert some particular state of affairs as the case. to make a claim that can be judged true or false and hence will be involved in any proposition we make about the world. The logical constants.512). have in common. and makes use of it in his characterization of the general form of the proposition: it serves as a way of expressing just the essential interconnectiveness of all our means of representing the world. Thus. given any picture. (to inﬁnity) are constructed” (TLP 5. everything we can say about the world is in some sense laid out in advance – we know at once all the possibilities of the existence and nonexistence of atomic facts that it could represent. But this then suggests that to understand denial we must also understand all the other logical constants.” “ p & p. that is. as the means of specifying various subsets within that set of possibilities presented by the picture. as Wittgenstein later points out. just because the capacity to say something true or false could be seen in this way to depend on a prior set of unasserted possibilities that Wittgenstein in the Notebooks connects his conception with (what he understands as) Frege’s idea of the “assumption”:
Although all logical constants must already occur in the simple proposition. emphasis mine). It is.” “ p. as will “ p v p.42.” and so on: “That which denies in “ p” is however not “ . Hence the common rule according to which “ p. etc.” but that which all signs of this notation. For. They allow us. Thus Wittgenstein remarks on how the proposition “reaches through the whole of logical space” (TLP 3.” “ p v p. Wittgenstein’s basic thought here would thus seem to be that. its own peculiar proto-picture (Urbild) must surely also occur in it whole and undivided. say. any means of depiction. Then is the picture perhaps not the simple proposition. I suggest. of Principia Mathematica. but rather its prototype (Urbild) which must occur in it? Then. which deny p. he regards the possibility of the Sheffer stroke (which by itself constitutes a truth-functionally complete set) as of great signiﬁcance. this prototype is not actually a proposition (though it has the Gestalt of a proposition) and it might correspond to Frege’s “assumption” 83
. too.” “p p.The essence of the proposition Now although there is one sign for negation in the language.6 and in every context in which they could occur. “ p” will represent this same fact.

7 But with the above discussion. rather. At the same time. a form that is common to both. Wittgenstein.” the so-called judgment stroke). a clear understanding of this idea makes evident that we have no hold on that form apart from our capacity to make true and false statements about the world. A black spot on white paper. the form of the spot can be described by saying of each point of the plane whether it is white or black. Rather.Wittgenstein’s Tractatus
(Annahme). must be understood essentially as coopting the Fregean insight. which he refers to not only in the Notebooks but also at 4. this is by no means to suggest that Wittgenstein’s thinking here should simply be assimilated to Frege’s. To the fact that a point is black corresponds a positive fact. taking what he sees as important in Frege’s approach and using it toward a very unFregean end. Just this idea would seem ultimately to lie behind remarks 4. assert something as the case – we might well regard the proto-picture as akin to the Fregean “assumption. to the fact that a point is white (not black). (NB 29–30)
Wittgenstein is here presumably referring to Frege’s claim that a judgment involves a movement from a “mere combination of ideas” (BEG 11) – an unafﬁrmed thought marked in the Begriffsschrift by a horizontal stroke – to a statement that is asserted as true (which in the Begriffsschrift will then be prefaced by “| . What is important in the notion of the assumption for Wittgenstein is that it brings out how the possibility of saying something determinate about the world depends logically on a prior inner connection between language and reality. “picture”) to explain the concept of truth. or.063 and 4. What the Notebooks passage calls the “proto-picture” would seem to be equivalent to the existent and nonexistent atomic facts that the picture presents.”8 Of course. In that case the proposition would consist of proto-pictures. the connection to Wittgenstein’s own concerns should now start to become clear. which were projected on to the world.064. what is common to those facts. a negative fact. Since it is only with the determinate method of projection provided by the logical constants that the picture can represent a particular state of affairs – that is.063 of the Tractatus. If I indicate a point of the plane (a truth-
84
. Commentators have long been puzzled about Wittgenstein’s interest in (and interpretation of) this Fregean idea. which I think it is useful to quote in full:
An illustration (Bild. in his characteristic way of responding to his predecessors.

It is then against the background of this common pictorial space that the picture can be projected so as to specify a determinate state of affairs.064)
Now Wittgenstein’s conception of truth will be discussed in more detail shortly. we recall. But it would be easy to conclude from these passages that he is primarily concerned to advance an extreme form of veriﬁcationism. for it signiﬁes no thing (truth-value) whose properties are called “false” or “true”. Wittgenstein here points out that the possibility of making a determinate assertion in the case at hand
85
. and thereby I determine the sense of the proposition. “logic must take care of itself. the verb of the proposition is not “is true” or “is false” – as Frege thought – but that which “is true” must already contain the verb. But to be able to say that a point is black or white. is that the Form der Abbildung. assertion cannot give it a sense. etc. (TLP 4. Then. The claim at 2. I must ﬁrst know under what conditions a point is called white or black. runs fundamentally counter to what we have described as Wittgenstein’s conception of the self-sufﬁciency of sense. we must view this passage in connection with his earlier discussion of the picture. etc.473.The essence of the proposition
value in Frege’s terminology). And the same holds of denial. is identical in the picture and what it depicts: because the pictorial elements have the same possibilities of combination as the objects for which they go proxy the picture will always be a picture of the world. the notion that.17. however. that his contention is that for a proposition to have a sense we must ﬁrst lay down some sort of rule specifying the conditions under which it is to count as true. the pictorial form. etc. in order to be able to say “p” is true (or false) I must have determined under what conditions I call “p” true. (TLP 4. this corresponds to the assumption (Annahme) proposed for judgment. The point at which the simile breaks down is this: we can indicate a point on the paper. In the terms of the above passage. but to a proposition without a sense corresponds nothing at all. as he puts it at 5. without knowing what white and black are. this idea could be expressed by saying that it is only given the possibility of identifying a location on the piece of paper (the analogue to the Fregean Annahme) that I can assert that a given point is black or not black.”9 Instead. for what it asserts is the sense itself. just as the possibility of representing a state of affairs requires a particular way of projecting the picture. Such an idea.063) Every proposition must already have a sense.

of specifying a sense. to have a proposition is just to have provided ourselves with the means of arriving at what could be the case. that they must be conceived as in some sense operations on a pregiven content.” For to hold that the proposition already has a sense.131 to characterize the relation between the pictorial elements and the objects with which they are correlated. or that the whole of logical space is given along with the picture (and what it presents) is to suggest that the logical constants do not introduce anything new into our understanding of the world. if more awkward. describes what it means to have a proposition in the ﬁrst place: the proposition is the setting forth of a possibility of a state of affairs. Thus. Once we have the picture with its intrinsic connection to the world. Through this discussion we then begin to see the thinness of the notion of a “logical constant. rather. there is nothing that corresponds to the assumption in the case of the proposition without a sense – we do not ﬁrst point to a region in logical space and then decide whether it or its negation is to be asserted. This. particularly given my own translation of darstellen by this word. Instead. It then becomes apparent that Wittgenstein’s point is that the logical constants cannot be construed
86
. That the logic of the facts cannot be represented” (TLP 4. translation. since (as we have seen) the term vertreten is also used at 2.0312). however. is not analogous to some special stipulation that must accompany the proposition but.10 That is why Wittgenstein emphasizes that. Wittgenstein says that the genuine proposition already has a sense – no further move is required for it to represent a determinate state of affairs. the identifying (with the help of the logical constants) of a particular region in logical space. is to suppose that this “pregiven content” is itself a kind of determination of reality. Hence Wittgenstein’s oft-quoted remark: “My fundamental thought is that the “logical constants” do not represent (vertreten). What Wittgenstein sees Frege as (appropriately) reaching for with his talk of the “entertaining” of a thought is then the idea that the logical constants cannot accomplish this end on their own. Frege’s confusion.Wittgenstein’s Tractatus demands our knowing what it means for a point to be black or white. it would seem that everything that is of signiﬁcance for logic is already given: logic comprehends only how reality becomes determined. unlike in the analogy of the spot on the paper. rather than only the condition of such a possibility. I suggest that “deputize for” or “stand for” would be a better. Now Ogden’s rendering of vertreten here as “represent” is somewhat misleading. however.

Just as the Bedeutungen of the names were seen to be
87
. is the “nonrepresentativeness” of the logical constants held to be such a central point? Part of the answer. the logical functions cannot be construed along the lines of genuine (material) functions.” and so on stand for anything. in a manner analogous to his treatment of the elementary propositions. one may wonder why this claim of Wittgenstein’s should constitute his “fundamental thought. has to do with the sort of move that Wittgenstein is here making. Russell’s approach.” “or. He in fact goes so far as to compare the attempt to grasp the fundamental concepts of logic with the search for Neptune. the misguidedness of the philosopher’s demand more generally. “with the difference that the ﬁnal stage – the search with a mental telescope for the entity which has been inferred – is often the most difﬁcult part of the undertaking” (Principles xv). the true import of Frege’s distinction between assumption and assertion is just the dismantling of the most fundamental Fregean idea – the idea that “logic” constitutes a genuine subject matter. Indeed. he really must be understood as attempting to show. too. Nor is this a point directed merely at Frege. that it makes no sense to suppose a domain of entities which form the special province of the logician. given the pictorial nature of the proposition. Perhaps the undermining of this assumption does call into question the “Platonism” inherent in the Fregean and Russellian approaches – but that alone would hardly serve to cast aspersion on the sum total of their contributions. then. there is surely much more going on in Frege and Russell than the bare assertion of the existence of such entities. Still. is called into question with the Tractatus’ attempt to deﬂate the reality of the logical constants. For Wittgenstein. as is evident in his previously referred to claim that “the chief part of philosophical logic” is “the endeavor to see clearly the entities” that mathematics regards as indeﬁnable (Principles xv).” Surely there is more at issue in the Tractatus than whether or not “and. Russell is even more explicitly committed to the assumption of a deﬁnite logical subject matter. We are meant to see that. are then at once able to represent the full range of possible facts – no logical coordination is necessary. We correlate elements of the proposition with objects and. then.” “not. contrary to Frege’s contention. at least. Why.The essence of the proposition as names. as additional elements of the proposition to which there must correspond anything in the world. For in holding that nothing corresponds to the logical constants.

” as the particular ways that the propositional sign is projected on to the world. Wittgenstein is then suggesting that the attempt to “look for” a logical entity of the Fregean/Russellian variety is not a mere vain endeavor – as if he were claiming. is nothing but some state of affairs (a possible fact) that the proposition can represent.” it would appear. the Tractatus’ Grundgedanke is explicitly anticipated in the remarks that close the 3s:
The proposition determines a place in logical space: the existence of this logical place is guaranteed by the existence of the constituent parts alone. the sorts of questions that Wittgenstein takes Frege and Russell to be concerned with) and in this sense to be its “fundamental” thought. constitute part of the means by which that stipulation becomes possible.Wittgenstein’s Tractatus absorbed into the way the propositional constituent functions in the propositions in which it can appear.4) The propositional sign and the logical coordinates: that is the logical place. Indeed. to use Russell’s analogy. (TLP 3. But that is to say that the logical constants.41) The geometrical and the logical place agree in that each is a possibility of an existence. And that makes it evident that the ultimate point here is much the same as the one that emerged in the discussion of the analysis of the elementary proposition. The logical constants or “logical coordinates. The move against the logical constants can thus be said to be paradigmatic of the Tractatus’ way of dissolving the questions of philosophy (in particular. it is one position within the overall coordinate system that Wittgenstein calls logical space. In asserting that such a place is “guaranteed” by the existence of the signiﬁcant proposition. instead of constituting some features of reality that might themselves be described. by the existence of the signiﬁcant proposition. (TLP 3. simply
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. Wittgenstein must then be seen as again emphasizing the internal nature of the relation between a proposition and what it represents: the proposition is nothing but the stipulating of a location within a larger framework and hence cannot but pick out a logical place. that the location in space in which we hoped to ﬁnd a planet is in fact empty – but a chimera: it is nonsense to suppose that an “it” could ever satisfy our search. (TLP 3.411)
The “logical place. so the logical constants are incorporated into the means by which the propositional sign as a whole is compared with reality.

89
. so too with logical space and the logical picture.The essence of the proposition form part of the logical coordinate system within which genuine descriptions are made. For this is simply a way of pointing out that it is the same picture that allows us to say A and also A. in other words. A & B as well as A v B. But the general direction of his response should already become apparent when we recall what it really means for him to say that the picture presents the existence and nonexistence of atomic facts. while this image brings out rather strikingly how the logical constants cannot be blithely included in amongst the other elements of the world. is the necessary by-product of our ability to represent the world. The “ﬁeld” of what a picture presents – logical space itself – then grows out of. assumes from the start the notion of the picture in use. The existence of logical inference. is parasitic on. in a certain sense. This is not to deny that.42. The case. Still. it may appear to do so at the price of assuming a very inﬂated conception of “logical space. by means of the logical constants. we must remember. and so on: the whole account of the picture. the contours of logical space can be described in advance. Thus Wittgenstein. what that picture can represent.” For does not the notion that the whole of logical space is somehow “given in its entirety” with the possibility of a proposition express nearly everything that philosophers have traditionally meant when they have held logic to be a priori? Has Wittgenstein then not simply transposed the question of the nature of the supposed logical entities to one about the nature of this mysterious a priori coordinate system – logical space? In fact. one sentence after declaring that the “whole logical space must already be given” by the proposition. The idea of the coordinate system is thus again central in Wittgenstein’s attempt to show the emptiness of the philosophical enterprise. adds: “The logical scaffolding round the picture determines the logical space” (TLP 3. emphasis mine). Logical space. is in many respects the same as with physical space: just as we saw that the form of physical space does not constitute an a priori constraint on our ability to represent the world but. we might say. rather. Wittgenstein’s full answer to this question is bound up with his understanding of the logical constants as operations and hence must await our discussion of the speciﬁcation of the general form of the proposition. emerges out of the signiﬁcant use of the spatial picture.

thought (gedachte. depends on such a possibility. And that. at 3. thought.11 But. will mean precisely showing how little the a priori comes to: it comprehends no more than our characteristic methods of projecting the pictorial fact on to reality. for him.
III
Here. It might well seem that Wittgenstein. Wittgenstein’s aim is thus not to deny altogether the traditional idea of logic as a priori. Indeed. the same possibility allows Wittgenstein himself to offer his own general characterization of the proposition.Wittgenstein’s Tractatus as the Tractatus understands it. Wittgenstein follows the above quoted series of claims with a remark about the “applied.1) 90
. but to attain greater clarity with regard to that notion.
In the proposition (Satz) the thought is expressed perceptibly through the senses. though. in a manner reminiscent of Frege. Tractarian readers of a certain mindset may well balk. is fundamentally committed to the assumption of a kind of mental intermediary between language and the world – that it is indeed against precisely this picture that much of the anti-mentalism of the Investigations is directed. explicitly equates thinking with a kind of projection.11. (TLP 3. as it were. propositional sign” (TLP 3. For I seem to be suggesting that talk of “projection” constitutes.5) and. the projection of the proposition. We must then examine more closely Wittgenstein’s way of connecting the notions of proposition. the end of the story for Wittgenstein – as if seeing how the logical dimensions of the proposition are incorporated into the projecting of our pictures were akin to those dimensions’ vanishing from the radar screen of philosophical consideration.13 To attribute this conception to the Tractatus would give its move against the assumption of genuine logical constants a quite different character than what I have been suggesting. the central purpose of that characterization is to make clear how we nonetheless cannot understand the dimensions of logical space entirely apart from the use. as we shall see. But doesn’t the Tractatus in fact hold that the possibility of projection itself requires explanation? And is the notion of “thinking” not introduced to fulﬁll just this function?12 After all. “thought-through”). and projection.

made manifest. And the proposition is the propositional sign in its projective relation to the world. the proposition (Satz). The method of projection is the thinking of the sense of the proposition. genuine existence of the Gedanke.” hovering over the propositional sign. (TLP 3. has both a sense (Sinn) and a reference (Bedeutung). (der sinnvolle Satz. of communication in general – is to be secured. Far from adopting a Fregean model of the relation of thought and propositional sign. just by means of the proposition that the thought is expressed. to propose a counter theory in which the thought is “immanent” in the propositional sign. His ultimate aim. it begins to seem as if the Tractatus is essentially concerned to advance a diametrically opposed conception. Thus. The contrast of this approach with Frege’s is at once apparent. like the name. The proposition’s Bedeutung is a truth value. its Sinn. In introducing the notion of the projected propositional sign. it is. For Frege (post-1892). we might then suppose. rather than having two entities – the thought and the propositional sign – and then worrying over how they are to be connected. The proposition. since then it would constitute its Bedeutung – Frege over and over insists on the independent. TLP 4)
The thought – the logical picture of the world – is in these passages presented as intimately connected to the proposition. we might say. a vaporous “proposition. a thought.The essence of the proposition
We use the sensibly perceptible sign (sound or written sign. this assumption is unavoidable if the objectivity of language – which is to say the possibility of science. for Wittgenstein the thought would seem to emerge precisely in and through the projection of the propositional sign on to reality. But to put the matter this way is now to overstate Wittgenstein’s difference with Frege – or. While the relation between a propositional sign and a thought is on this account somewhat obscure – the latter presumably cannot be named by the propositional sign.11) The sign through which we express the thought I call the propositional sign.12) The thought is the signiﬁcant proposition. is just to restrict Frege’s extravagant ontology. (TLP 3. etc. cannot be understood apart from the propositional sign in its signiﬁcant use.14 For him. Wittgenstein would appear to be suggesting that it is simply unnecessary to assume the existence of a separate thought. rather.) of the proposition as a projection of the possible state of affairs. in turn. to misdescribe the real character of
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.

for the latter. rather than ontological terms. except what was contrary to the laws of logic. these passages have a distinctly Fregean ring to them. Now such an interpretation is.031) That logic is a priori consists in the fact that we cannot think illogically. the remark about the impos92
. The nature of this shift is already apparent in the remark following 3. (TLP 3. One solution to these interpretational difﬁculties would be to see the Tractatus as retaining the Fregean notion of thought. (TLP 5. correct as far as it goes. The truth is. in particular hearkening back to the Grundgesetze discussion of our supposed inability to understand beings “whose laws of thought ﬂatly contradicted ours” (BLA 14).4731)
Indeed. but. That is. its central aim is always to shift our understanding of what that normativity comes to.03) It used to be said that God could create everything. But even here we must caution against a too facile incorporation of Wittgenstein’s views within a Fregean framework. For while the Tractatus retains Fregean language regarding the normative status of logical laws. since one might well argue that. (TLP 3.031. I would suggest. In this sense he could be said to be getting at the heart of Frege’s view. however. is not only very foreign to the Tractatus in general but also speciﬁcally ignores the extent to which Wittgenstein seeks to accommodate a notion of objectivity within his conceptions of thought and thinking:
We cannot think anything unlogical.15 Wittgenstein’s relation to Frege on the issue of the nature of thinking evidently cannot be construed in terms of ﬂatly opposed positions. For one thing.Wittgenstein’s Tractatus that difference. for otherwise we should have to think unlogically. it appears to leave Wittgenstein open to the charge of subjectivism (one thinks here of Frege’s objections against formalism): to simply deny the existence of the Fregean Gedanke would seemingly be to reject the objectivity it is supposed to guarantee. the real criterion of identity for thoughts ultimately is given by a sentence’s role in logical inference patterns. purging it of any connection with ontology. The embrace of subjectivism. Wittgenstein is to be understood as seeking to account for what one might think of as the objective dimension of language – in effect. we could not say of an “unlogical” world how it would look. in effect. the possibility of successful communication – but to express that only in logical.

We might then express Wittgenstein’s general stance toward the notions of thought and thinking in this way. Once more. are given together. is that to specify coordinates on a graph is to specify a point. but that is just because the projecting of the pictorial fact on to reality – its being thought – structures this space. Thinking permeates the picture – and so the possibilities for one of these notions cannot but coincide with the possibilities for the other. Of course we think. the logical coordinate system: thinking and logic. we could say. and the pictorial fact (the possibilities of which constitute logical space) on to reality. But that at the same time expresses the
93
. What Wittgenstein aims to bring out is how the signiﬁcant proposition with which we begin any analysis is already “thought. informs every aspect of his discussion of the picture: the picture’s capacity to represent some particular state of affairs presupposes the projecting both of the pictorial elements (the possibilities of which constitute the picture’s Form der Abbildung). though. or to give the co-ordinates of a point which does not exist” (TLP 3. Wittgenstein thus attempts to preserve the Fregean insight about the impossibility of illogical thought – even.” how we start out with “the propositional sign in its projective relation to the world. to get at the heart of what he takes to be Frege’s concern. The real question concerns the signiﬁcance of this truism. he is not concerned to dispute the assertion that there is thinking. Why can’t we give the coordinates of a point which does not exist? The answer. as we have seen. it becomes apparent how. The same will then be said to hold with regard to “thinking” and “region within logical space. that the propositional sign is not capable of interpreting itself. the suitability of the notions of thinking and thought for use as central tools of philosophical analysis. identiﬁed.The essence of the proposition sibility of illogical thought quoted above: “To represent (darstellen) in language anything which ‘contradicts logic’ is as impossible as in geometry to represent by its co-ordinates a ﬁgure which contradicts the laws of space. or rather could be. for the Tractatus. of course. as I suggested above. the necessity that is said to belong to thought’s respecting of logical boundaries comes at the price of the utter emptiness of this claim.” We might assert that to think is always to specify a region in logical space. but is simply a way of bringing out that we do not have a notion of a point apart from the way it is.” This idea. This is not to attribute some magical creative properties to such a speciﬁcation. the exposing of the heart of a philosophical question is equivalent to its disappearance.032). Clearly.

instead of. Far from postulating a mental bridge connecting the picture to reality. 2.” These central terms are introduced at the close of Wittgenstein’s initial discussion of the picture. we must come to understand how. as Hacker suggests.221: “What the picture represents is its sense (Sinn). however.2. as we have seen. We shall address this issue through a consideration ﬁrst of the Tractatus’ notion of tautology and then of its speciﬁcation of the general form of the proposition. so to speak. however. for Wittgenstein.”17 It appears from 4.16 Wittgenstein suggests that it is the mental realm itself that needs to be accessed – and the way is via the picture. we can characterize this latter notion and what such a characterization comes to. the picture is also said to “represent” some particular state of affairs in logical space. in other words. This proposition has such and such a sense. that I only know a proposition’s sense when I know what it means to be true and false: “The sense of a proposition is its agreement and disagreement with the possibilities of the existence and nonexistence of the atomic facts”. a positive and negative fact. he suggests that the sense is given through knowing what obtains when the proposition is true: “In order to be able to say ‘p’ is true (or false) I must have determined under what conditions I call ‘p’ true.” Since. sense here includes all of a proposition’s truth-possibilities. when we recall from our earlier discussion18 that the Sachlage represented by the proposition is itself conceived as containing both an existent and nonexistent atomic fact – that is. 4. this suggests that such an assemblage of facts is to be regarded as the sense of that picture.Wittgenstein’s Tractatus weakness of our hold on the notion of thinking. than the logic it would clarify. This appearance of conﬂict disappears. if “thinking” will not play an explanatorily privileged role in the Tractatus’ discussion of logical space. Both of these notions may be approached through further reﬂection on the Tractarian conception of “sense” and its relation to “truth.
IV
Still. First. This proposition represents (darstellt) such and such state of affairs (Sachlage). then.” Which state of affairs is then to be identiﬁed with the picture/proposition’s sense? It may appear as if Wittgenstein gives conﬂicting responses to this question. is what Witt94
.031 conﬁrms the point: “One can say.063. The Sachlage. and thereby I determine the sense of the proposition. it brings out how “thought” is no closer to us. For at 4.

it should be clear that Wittgenstein cannot intend to maintain any such position. is not to suggest that there is no way in which the world and the picture can be compared. To represent a sense is then to highlight. it is just because some kind of comparison can be effected that we are able
95
. in which a body may be placed. orienting us in this way toward the facts with which it is associated. however. is to bring out the inseparability of the connection between the picture and reality. only structured or shaped. negative. that 4. as it were.” That is. Now taken in isolation.014 refers to as the “pictorial internal relation which holds between language and the world. he should then be seen really as stressing the ﬂip side of what 4. just as earlier he emphasizes how we can have no hold on “fact” apart from the particular means we use to represent the world. these claims may seem to commit Wittgenstein to a kind of realism of facts reminiscent of Russell’s logical atomism.144.20 After all. rather than endorsing a full-blown Russellian ontology of facts – positive. of course. the sense of a proposition is like an arrow. On the contrary.) In identifying a picture/proposition’s sense with a state of affairs. one of the twin aspects presented by the picture. to suggest that the fact is only given. Wittgenstein.1272 declares any talk of facts to be nonsense.19 But that highlighting always takes place against the backdrop of its complement – which is to say that an understanding of the proposition’s truth conditions carries with it an understanding of its falsiﬁcation conditions and vice versa. at this point he is stressing how our understanding of the nature of that means of representation is likewise inseparable from the facts toward which it is directed. and so forth – is thus from the start seeking to bring out the emptiness of this whole conception.The essence of the proposition genstein at 4. This. general. one might ask. therefore. is he not suggesting that a prior cognizance of a fact (or set of facts) is necessary to understand the picture’s sense – and. through the picture that depicts it. (We must not forget. after all. must be assumed to be brutely “out there”? And are not these facts regarded as responsible for “making” the picture (or proposition) true or false?21 Given what we have said about the ﬁrst part of the picture theory alone. we have seen. that facts. particular.063 likens to a solid substance and the space within it. As Wittgenstein remarks at 3. possible as well as actual. The pictorial elements and their real world counterparts are held to have the same possibilities of combination: the force of this assertion.

The “yes” or “no. is to show just the intrinsic connection between the picture’s content and the world: it is precisely because a possible state of affairs is. ﬁxing what we are to expect to the extent that. Once the picture is then projected in a determinate manner. That is why a picture represents its subject correctly or incorrectly. the picture can be said to stand “outside” its subject matter because the method of projection always operates on a completed picture.” The Form der Darstellung comprises the various ways of projecting the picture on to reality (the various ways. but it potentially misses the point. For this phrase might tend to suggest some sort of agreement between two distinct sets of facts.22 Given that this form is common to the picture and what it depicts. is thus really meant to drive a wedge between the notion of truth and any concern with sense and the conditions of representation (the proper concerns of the philosopher). that a picture can represent). corresponds to the picture’s truth or falsity. as I have indicated. as he puts at 2. the whole space of facts presented by the picture will necessarily belong to the world. (Its standpoint is its representational form [Form der Darstellung]). to enable us to say how things might stand – that how things are in fact is not something that can be gathered from the picture alone. as Wittgenstein later puts it. while Wittgenstein’s primary aim. Nonetheless. is to get us to see that the role of the picture is only to prepare us to meet reality. Wittgenstein’s purpose. we must recognize how we come to this point only after every move having to do with the logic of depiction has been taken. “contained” in the picture that any sort of agreement between the two can be realized. that is to say. on the pictorial elements taken against the background of the Form der Abbildung.023).173 helps to clarify this point: “A picture represents its subject from a position outside it.” of course. It may be helpful to reﬂect here on Wittgenstein’s alter96
.Wittgenstein’s Tractatus to speak of truth or falsity at all. rather than constituting part of an elaborate correspondence theory.” as is typically done. 2. “one only needs to say ‘Yes’ or ‘No’ to [the picture] to make it agree with reality” (TLP 4. it will represent exactly one state of affairs as obtaining. an easy call – it is simply a matter of looking.23 is then not wrong. The claim about the need to compare the picture and reality. But since what the world will look like in either case has been completely described beforehand. this verdict is. To refer to the Tractatus’ remarks about truth as constituting a “correspondence theory. in other words. as it were. so to speak.203.

” as the various ways in which the picture can be compared with reality. the space that is carved out by p is immediately ﬁlled in with the “solid substance” that bounds it. In the same way. see TLP 4. In the tautology the conditions of agreement with the world – the representing relations (die darstellenden Beziehung) – cancel one another.224–5). indeed sole. the resulting proposition thus leaves reality absolutely
97
. 5. To postulate an a priori true picture would be like postulating a measurement that is correct simply in virtue of its constituting a position on the measuring scale. while some method of projection is necessary if a proposition is to represent a particular state of affairs in logical space. Implicit in the picture theory. Now for the Tractatus the primary. A picture that does not require comparison with reality will eo ipso not represent a possible state of affairs in the world – that is. the “statements” of formal logic. if it is to have the chance of being judged as true. Wittgenstein makes this idea explicit at the close of his initial discussion of the picture: “It cannot be discovered from the picture alone whether it is true or false. will not have a sense – and hence will not be a genuine picture. 4. to build on Wittgenstein’s metaphor at 4. There is no picture which is a priori true” (TLP 2. the picture requires its corresponding reality. 4.463. if only from afar. in certain instances these methods come in conﬂict. so that it stands in no representing relation to reality. we construct a string of signs of the form p v p: it is as if. is Wittgenstein’s later disparagement of the sentences of logic – the “tautologies” and “contradictions” – as “senseless” (sinnlos.461. of course.132). the other none. examples of such a priori true pseudo-pictures are.4611. then. for example. Suppose. the possibility of its being compared to something outside itself.462 makes quite evident how this central idea of the Tractatus is connected with the earlier remarks about the picture:
Tautology and contradiction are not pictures of the reality. For the one allows every possible state of affairs.The essence of the proposition nate metaphor of the ruler. They represent (darstellen) no possible state of affairs.
The “representing relations. Wittgenstein is suggesting that. are equivalent to what we have earlier referred to as the methods of projection of the pictorial fact. But that is nonsense: we have genuinely taken a measurement – we can speak of “correct” and “incorrect” measurements – only when the ruler has been laid against some object in the world.

The very thing that allows propositions to express a deﬁnite sense can also serve. is a tautology and not a genuine proposition. “1 is a number. the good judgment to be able to recognize when the inner syntax of the proposition has been violated. from the standpoint of communication it is less than optimal. Wittgenstein says.” or “There are objects”) – have the appearance of ordinary sentences. in the same way that “0” is part of the symbolism of Arithmetic” (TLP 4.. We could say that the central purpose of the discussion of analysis in the 3s is in fact to make precisely this point: to hold that the forms of the elementary
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.4733).0031): just because “p v p” and “p v q” have superﬁcially the same form (rely on the same method of projection). in such cases. as I pointed out in the Introduction. like the propositions of logic.” but from a failure to construct a picture in the ﬁrst place. albeit in a somewhat different way. For this reason Wittgenstein denies that logical propositions can be completely excluded from a language: “Tautology and contradiction are.g.) Hence “p v p” will not say anything. it would seem. in part for this reason) he speaks of language as “disguis[ing] thought” (TLP 4. for example. This idea of what we might call the delicacy of sense is quite central and needs to be elaborated on. they are part of the symbolism. at least. not nonsensical (unsinning).Wittgenstein’s Tractatus untouched. First. Unsinnigkeit is said in the Tractatus to arise not from conﬂict between the picture’s “representing relations. “p v q” to represent. For this reason too (or.4611).002) and praises Russell for “hav[ing] shown that the apparent logical form of the proposition need not be its real form” (TLP 4. we should not at once assume that these are propositions of the same sort. (Although we might be pleased with such a result from an environmental perspective. Sense and senselessness spring from the same root and so care must be taken – thoughtfulness exercised – to tease them apart. The discernment of what Wittgenstein calls “nonsense” then requires a sensitivity to the multiplicity of logical forms. Indeed. To be sure. however. even while it relies on the same rules that enable. most of these pseudo-propositions – and certainly all those that Wittgenstein is chieﬂy concerned to expose (e.24 Nonetheless.25 they would not otherwise have the capacity to mislead. to deprive them of that sense. it should be noted that the basic point applies not only to the propositions of logic but also to the nonsensical claims of philosophy. “we have given no meaning (Bedeutung) to some of [the proposition’s] constituent parts” (TLP 5.

since. For we cannot have a general decision procedure even for all of ﬁrst order logic. all of this is simply a different way of putting what has been my fundamental contention throughout – namely.26 The Tractatus does not and could not attempt to provide us with an external mark of signiﬁcance. that its aim is always to undermine the central questions of philosophy from the inside. but quite another to suppose that. Still. the difﬁculties and peculiarities of this whole approach are particularly evident when we focus on the analysis of the propositions of logic.” But if this claim rests on the possibility of a general decision procedure for the whole of logic – if. But we must ask ourselves: How has this been accomplished? It is one thing to grant that a form of words cannot be recognized as a proposition of logic simply from its superﬁcial appearance. one must regard it as sinnlos. that the Tractatus’ method is essentially dialectical. perhaps “particular” would be better here) combinations of objects could correspond to them. without making appeal to any kind of ﬁxed criteria of sense and nonsense. as was shown by Church and Turing in 1936.466. once such a proposition has somehow been identiﬁed.” But why does the fact that “p v p” pictures no particular or determinate state of affairs necessarily prevent this expression from composing a legitimate combination of signs?27 Could we not equally say that such symbols just constitute very general pictures? One might suppose that Wittgenstein would buttress his argument with the claim in 6. propositions that are true for every state of affairs cannot be combinations of signs at all. Of course. Has Wittgenstein actually shown that the propositions of logic have this property? At 4. only determinate (bestimmte.
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. as representing no state of affairs. Wittgenstein appears to rely on this point as having been ﬁrmly established. and this fact contains in itself the whole philosophy of logic. he asserts: “In other words.The essence of the proposition propositions are not give a priori is just to suggest that sense is not given simply by virtue of a sentence’s assuming a particular appearance. all logical propositions fail to be pictures of the world for the reason that we are imagined to have an a priori test for their truth and falsity28 – then this part of Wittgenstein’s argument seems to fall to the ground.113: “It is the characteristic mark of logical propositions that one can perceive in the symbol alone that they are true. For it would seem that the assertion of the tautological nature of such propositions – the fact that they say nothing about the world – is central to the Tractarian response to the Principia and Begriffsschrift. if they were. that is.

Toward the beginning of that discussion Wittgenstein states:
Theories which make a proposition of logic appear substantial are always false. This now by no means appears self-evident. the possibility of truth and falsity and propositionhood are given together. Indeed our proposition now gets quite the character of a proposition of natural science and this is a certain symptom of its being falsely understood. that analysis also must reveal how the strings of logic are not genuine propositions in the ﬁrst place since. laying down conditions of material adequacy for an analysis of the logical proposition: any acceptable analysis must make evident how such propositions are not true and false like the “substantial” propositions of natural science. we need to consider the more extended discussion of tautology in the 6. (TLP 6. in other words. Indeed. of course. are internally related. no more so than the proposition “All roses are either yellow or red” would sound even if it were true. believe that the words “true” and “false” signify two properties among other properties. he starts off with the belief that this sort of proposition cannot be approached as if it were on par with a claim of natural science and then attempts to ﬁnd various means to make this distinction compelling. to declare the special nature of the logical proposition. One could e. and then it would appear as a remarkable fact that every proposition possesses one of these properties. any more than he has proven that the world (really) is all that is the case.1s. What is important about this passage. would appear to stand: How has Wittgenstein proven that logical propositions are senseless tautologies? The answer. is that it makes evident that Wittgenstein makes no pretense of being driven by certain previously unrecognized facts.111)
Here Wittgenstein is. to persuade us to look at “p v p” from other than this “false” (“misleading” would perhaps be a better word here) perspective. The recognition of something peculiar about the status of logical propositions is. in essence. is that he has not proven this. “proof” has no place in the philosophical space in which the Tractatus moves. by some overpowering argument. then. integral to the whole perspective the Tractatus
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. Rather. then.g. as he implies in this passage (and has earlier made clear in the discussion of the picture). as I have maintained throughout. But to grasp fully what this general point comes to in this case.Wittgenstein’s Tractatus The question.

the real question here concerns the basis of this convention or. But that would already seem to indicate that the Tractarian claim about those propositions’ tautological nature cannot be viewed simply as a self-standing assertion that awaits its proper justiﬁcation.”31 But. a point we alluded to above. we must ask ourselves what consequences this mistake would have. then. a number of commentators have assumed that the Tractatus’ whole position rests on the assumption of a general decision procedure.1203). Indeed. as well as claims like 6. the implications of adopting it. that we do have an effective method of determining validity for all of ﬁrst order logic.126 (“Whether a proposition belongs to logic can be calculated by calculating the logical properties of the symbol. in so doing. like Black. We then would stand in the same relation to the whole of logic as we do at present to the propositional calculus. It is in this context. he certainly does not seem to imagine himself as having provided a technique that is applicable to the whole of logic.113) about the “truth” of the logical proposition being perceivable in the symbol alone. counterfactually. of course. though. With regard to the latter we now can ask: does our ability to show that some sentence comes out true on every truth-value assignment to its component parts prove its tautologous nature? In a certain sense one may answer “yes. Are we.”32 Far from showing the emptiness of such expressions. that Wittgenstein makes the above-quoted remark (TLP 6. the Tractarian technique can be used to buttress an
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. Of course. Now because of this claim.” since it now has become customary (in large part as a result of the Tractatus) to take this as a deﬁnition of “tautology. forced to regard tautologies as senseless. perhaps better. even if he did assume that a general decision procedure were available. that it would prove “fatal to Wittgenstein’s philosophy of logic”?30 A consideration of this question will help to make clearer the Tractatus’ stance on this whole matter. pseudopropositions? It seems not. it is quite common to take the truth table method as revealing tautologies to be truths that hold in “all possible worlds. Must we conclude.”). Let us suppose.29 Regardless.The essence of the proposition seeks to articulate. Wittgenstein explicitly acknowledges that his “intuitive method” of exposing tautologies – a method that is essentially equivalent to the use of truth tables – is applicable “in cases in which no sign of generality occurs in the tautology” (TLP 6.

But that is not the conclusion to be drawn here. as if we might grasp via an act of intuition the tautological essence of the logical proposition. One might think that this would serve to explain why proof would be viewed as ultimately unnecessary in the case of recognizing tautologies. the same could then be said of all the propositions of logic. is precisely the force of the close of 6. where it is complicated. Instead.” Given the possibility of a general decision procedure. these remarks are difﬁcult and must be treated carefully. though.) Naturally this way of showing that its propositions are tautologies is quite unessential to logic.1121) – but even more so at
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. there are not some which are essentially primitive and others deduced from these.Wittgenstein’s Tractatus understanding of them as transcendent. must show without proof that they are tautologies. (And from a tautology only tautologies follow. This is evident in his dismissal of the philosophical signiﬁcance of psychology – “Psychology is no nearer related to philosophy. which again generate tautologies out of the ﬁrst. that the notion of showing is never used in connection with any such conjectured psychological state. Every tautology itself shows that it is a tautology. It would be easy to suppose that this talk of tautologies showing themselves as such rests on the possibility of some special moment of insight. Wittgenstein in fact is explicit in his denial of the relevance of psychological states to the issues with which he is concerned. the point is to see the independence of the question of the existence of a general decision procedure from the philosophical moral of the Tractatus’ remarks. from which the proof starts. Because the proposition.126:
We prove a logical proposition by creating it out of other logical propositions by applying in succession certain operations. It may appear as if I am now suggesting that Wittgenstein is unwittingly attempting to prove the opposite of what he had intended about the nature of the logical proposition.127)
Now. than is any other natural science” (TLP 4. I suggest.1262) All propositions of logic are of equal rank. “super truths. (TLP 6. (TLP 6. We have seen.
Similarly we ﬁnd:
Proof in logic is only a mechanical expedient to facilitate the recognition of tautology. This. it is to start to bring out how uncomfortably the notion of proof ﬁts in this context.

is not that this is an inadequate method of proof that is to be scrapped in favor of a generalized version of the truth table method. but that is no experience.31 and 4. I suggest instead that we view these remarks as reﬂections on what it means to call something a tautology. Such a procedure is followed in the “old logic. Indeed.431. To be sure. the systems of Frege and Russell. a tautology is instead part of what a particular linguistic form is. E. For Wittgenstein.” Invoking magical ﬂashes of insight will be of no use to Wittgenstein (or to us) in clarifying how logical propositions can be said to show their tautologous nature. however.33 While the truth table method may more clearly display the uniform character of a certain class of propositions.” as Wittgenstein calls it in “Notes Dictated to G. but that something is.126) – that is. This point can be made clearer through a consideration of the nature of the signiﬁcant sentence’s content. once more we see that it makes no sense to speak of proof in connection with the ascription of the term “tautology” to a proposition. Wittgenstein says that one way to prove a proposition of logic is by generating it from other such propositions by the application of certain formal rules. it would seem that we misunderstand the Tractatus’ use of this term if we imagine it to refer to any sort of “property” that may or may not be found to belong to a proposition. as we shall discuss shortly. with their reliance on axioms and rules of inference. But their method fares no worse than the Tractatus’ in terms of what it actually proves about the nature of the logical proposition: in either case. Wittgenstein shows how the proposition’s “truth conditions” – what we have seen to be the sense of the proposition – can be set out in the
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. with the way they function in our language. Wittgenstein is suggesting. that it is of a certain form.The essence of the proposition 5. that it can be grouped along side certain other linguistic signs. tell us what that character comes to. are viewed as giving us a misleading conception of the nature of logic. His contention here. Moore in Norway”(NB 109) – that is. all that is shown is that a given proposition “belongs to logic” (TLP 6. the real point is that this “mechanical expedient” does not. the formal systems of the Principia and Begriffsschrift (and Grundgesetze).552: “The ‘experience’ which we need to understand logic is not that such and such is the case. Such forms “show themselves” to be tautologies just because having this nature is bound up with the entire role that they play. any more than an axiomatic method of proof. At 4.

then “the last column is by itself an expression of the truth-conditions” (TLP 4. Wittgenstein explicitly draws the connection between these ideas at 4. Wittgenstein must not be understood as thereby suggesting that “(TTFT) (p.q)” and “p q.” On the contrary. what the Tractatus is suggesting is that we stand in the same position when we ask for the sense of a proposition as when we ask why it is tautologous. In the same way that the signiﬁcant proposition shows its sense. Thus the truth possibilities of the elementary propositions and various combinations of their resulting truth values are listed. Instead. as
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.34 But that means that the philosopher’s interest in sense – the desire for a proper speciﬁcation of what that sense is – cannot ﬁnd its fulﬁllment in either of these expressions as such. then. that it somehow constitutes what we really mean when we assert “p q. be clear on the nature of this analogy. for certain purposes or in certain contexts. and the truth functional nature of the molecular proposition made perspicuous. for Wittgenstein. the logical proposition can be said to show that it is a tautology. simply replace the second. Of course.4). For the point is not that being tautologous is. the tautology and the contradiction that they say nothing. This desire is instead satisﬁed by seeing what is common to these symbols and all others that could replace them. the ﬁrst can. what “p” “really” says emerges just through the possibility of translating between equivalent means of expressing this same sense. the truth table can itself be construed as an expression. that which the logical proposition says – the latter. since it is sinnlos. however. does not say anything.q)” is the preferred expression. He remarks: “A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions” (TLP 4. only shown. And at 4. in both cases one can offer some sort of response to this question: to a confusion about p’s sense we can. are equivalent expressions.461: “The proposition shows what it says.442) and constitutes a propositional sign.022 and 4.” We must.431: “The proposition is the expression of its truth-conditions” (emphasis mine). “(TTFT) (p. The sense of “p” is. his point here is just to bring out the deceptive nature of this demand for the “real sense” of a sentence. Now it is important to emphasize that. like the sense of a genuine proposition.Wittgenstein’s Tractatus now familiar form of a truth table.” he is suggesting.461. Certainly. as Wittgenstein asserts at 4. If we standardize the ordering of the truth-possibilities of the elementary propositions in the truth tables.

by terming the former a tautology. is as dialectical a move as any other in the Tractatus.126. one might say. Instead.126 calls “calculating the logical properties of the symbol. like all of the remarks in the 6. is just to grant that the assertion about the tautologous nature of the proposition of logic. in turn. from the desire for insight into the world’s essential nature that it bespeaks. provide alternate ways of saying the same thing. It is in the acknowledgment of this point that we see the incoherence of asking for an ultimate justiﬁcation for the ascription of “tautology. To grant this. nothing hidden from us. an attempt to offer an overarching characterization of logical truth. in its particular way of distinguishing such linguistic forms from signiﬁcant utterances. What this suggests. the text’s claims about tautology have no standing whatsoever.” If we consider this phrase by itself. One means the text has of drawing this distinction involves the possibility of what 6. no new facts that need to be brought to light.” for some underlying something to which we can appeal. is that the Tractatus’ whole point in this context is contained in the details of its account of the propositions of logic. similarly. however. 105
. urging us to take that difference in a certain way. Wittgenstein’s real aim in this whole discussion is only to draw our attention to a difference of form: he is emphasizing how unlike the role of “p v p” is from that of “p v q” and. it is quite natural to suppose that Wittgenstein is here referring to something like a decision procedure.35 But 6.The essence of the proposition I have just been emphasizing.” the assimilation that Wittgenstein sees as lying at the heart of Frege and Russell’s conception of logic as a science of maximally general truths. Let us look at this passage now in its entirety:
Whether a proposition belongs to logic can be calculated by calculating the logical properties of the symbol. rather than being put forth as a self-standing claim. There is. Shorn from the interplay with such a tendency. It takes its signiﬁcance precisely from the tendency to assimilate “p v p” and “p v q. must be read in light of the Tractatus’ discussion of the picture and its subsequent account of analysis. we have seen that Wittgenstein holds open the possibility of a number of different methods of exposing tautologies (of what at 6.1263 he calls “proof[s] in logic”).1s. But the key idea is that all such answers would seem to stand on the same level as what is questioned about.

” Rather than asserting something about what must be the case for every possible proposition of a certain form. We prove a logical proposition by creating it out of other logical propositions by applying in succession certain operations. he is only concerned to describe what happens in those instances where a proof is available. Because the propositions. as he would if he were relying on the idea of a general decision procedure. just like the Bedeutungen of the names. then it must be provable by logical properties of the symbol. from which the proof starts. the possibility of recognizing such a property is signiﬁcant. On the contrary. “rules dealing with signs”).
Notice. ﬁrst.Wittgenstein’s Tractatus
And this we do when we prove a logical proposition. He does not say that if anything is a proposition of logic.37 Of course. we form the logical propositions out of others by mere symbolic rules (Zeichenregeln. (And from tautology only tautologies follow. In speaking at this juncture of a “property of the symbol. For it necessarily involves focusing on the use of the picture as a pictorial whole or fact – the ways that it can “represent.” Wittgenstein would then seem to have moved up a level – he is concerned with what is common to a number of classes of propositions. will involve the recognition of a feature of the symbol. We saw that the symbol can serve as a way of showing what is common to a particular class of propositions and thus of characterizing the meanings of the names. we recall that a symbol or expression for Wittgenstein is any part of a proposition that contributes to its sense and that it is properly presented by a variable.” in the Tractarian sense of the term. Nonetheless. For without troubling ourselves about a sense and a meaning. must show without proof that they are tautologies. the structure of Wittgenstein’s claims. We can refer to properties of symbols only when we ignore everything having to do with the inner constitution of some class of propositions (their particular logico-pictorial forms) and consider no more than what is common to
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. a second order variable). say. there is for Wittgenstein no logical hierarchy of variables. Any such proof.) Naturally this way of showing that its propositions are tautologies is quite unessential to logic [emphasis mine]. this higher order property will be signiﬁed simply by a variable (rather than by. he only speaks of what happens “when we prove a logical proposition. since. he suggests. as I have suggested.36 Now. which again generate tautologies out of the ﬁrst.

truth is determined just by showing how a proposition is constructed. The point can also be seen. this point is evident when we consider a proof via the use of a truth table: this device allows us to see clearly that the truth of. the nature of their connection to reality begins to become clear. while the propositions of logic only show formal aspects of language and reality38 (indeed.” but only how the proposition is constructed. it would seem.121 makes clear that it is the genuine proposition that shows logical form).12. At 6. In order that propositions connected together in a deﬁnite way may give a tautology they must have deﬁnite properties of structure.
This passage suggests that Wittgenstein’s point is not simply. For. 4. as I implied above. Wittgenstein puts it this way:
The fact that the propositions of logic are tautologies shows the formal – logical – properties of language. say. that genuine propositions state something. of the world. what allows them to represent some particular state of affairs in the ﬁrst place. by reﬂecting on the axiomatic style of proof characteristic of the Frege and Russell systems – in fact it is the latter that Wittgenstein appears to have chieﬂy in mind in this passage. proof in the Principia is simply a matter of demonstrating that one linguistic form can be generated out of another solely through the application of “rules dealing with signs. he says that the fact that the propositions of logic are tautologies is what shows those aspects. Certainly. The Sinnloskeit of the logical proposition is then key: it is just through the disintegration of sense that results from the attempt to combine certain strings of signs into propositions that particular internal features of language/
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. as is often suggested. too. That its constituent part connected together in this way give a tautology characterizes the logic of its constituent parts. That they give a tautology when so connected shows therefore that they possess these properties of structure. Unlike in the case of the signiﬁcant proposition. The Tractatus’ claim is then that proof of the logical proposition relies on this common element alone. “p v p” can be determined with reference only to the truth possibilities of this propositional schema (its mode of projection). however. Given this way of construing the propositions of logic.” Here. according to Wittgenstein.The essence of the proposition their capacities to be projected across logical space – that is. we do not take into account the speciﬁc content of “p. Rather.

g. for Wittgenstein.Wittgenstein’s Tractatus reality come to the fore.1264 of the Tractatus: “The signiﬁcant proposition asserts something. Wittgenstein is claiming.1201: “That e. since they ultimately constitute no more than certain means of describing an already given propositional class. Such “propositions” can only show. That “(x). variables – variables that reﬂect properties of the symbol. And that. at 6.fx. for Wittgenstein. stamp some class of genuine propositions. in logic every proposition is the form of a proof.” Nothing can underlie the recognition of tautology because it is that very tautological nature
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. The same point is made. As one might put it. Every proposition of logic is a modus ponens represented in signs. That the proposition “p q.” “p” and “q” connected together in the form “(p q) & (p): : (q)” give a tautology shows that q follows from p and p q. albeit somewhat more obscurely. But this is to suggest that the propositions of logic are.” The proposition of logic serves to. as it were. To say that. to show how the members of that class share a particular form. not propositions at all. the tautologousness of such propositions is regarded as basic. to bring out a certain feature they have in common. and its proof shows that it is so. For this is simply to bring out that the proposition of logic serves as itself a way of characterizing. the properties of the symbol.” This is precisely the view that is put forward in the Notebooks: “Logical propositions are forms of proofs: they shew that one or more propositions follow from one (or more)” (NB 109). for example. (And the modus ponens can not be expressed by a proposition).” What his examples bring out is that the internal features of language and reality with which he is here concerned. but only serving as a way of characterizing what a number of (genuine) propositions have in common. The full force of these considerations is then felt with the illustration that Wittgenstein provides at 6. We thus see even more clearly why. to recognize a string of signs as a tautology is to recognize that that string is not itself attempting to say something. the proposition “p” and “ p” in the connexion “ (p & p)” give a tautology shows that they contradict one another. are nothing other than what we normally think of as inferential connections between propositions. as a paradigm in this particular “language-game.fx: :fa” is a tautology shows that fa follows from (x). etc. “(p q) v (p q)” is a tautology is simply to describe a given class of propositions. is all that we are doing when we say that “q” follows logically from “p” and “p q. as we implied above. etc. but.

Still. What he
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. or rather they represent (darstellen) it. They presuppose that names have meaning (Bedeutung) and that elementary propositions have sense. but rather one in which the nature of the absolutely necessary signs speaks for itself. Herein lies the decisive point. Wittgenstein connects this point with the fact that “we often feel as though ‘logical truths’ must be ‘postulated’ by us” (TLP 6. This same idea is elaborated on at 6. But that is precisely because the values of this variable are propositions: in describing them we ipso facto describe something about the reality with which they are concerned. And this is their connection with the world. It is clear that it must show something about the world that certain combinations of symbols – which essentially have a deﬁnite character – are tautologies. If we know the logical syntax of any sign language. at the price of any interest in pointing it out. But Wittgenstein wants to bring out how it is nonetheless misleading to describe matters that way: “We can in fact postulate [the ‘logical truths’] in so far as we can postulate an adequate notation” (TLP 6. depend for their life on what we do. Instead.1223). then we have already been given all the propositions of logic. in some sense.124:
The logical propositions describe the scaffolding of the world. something not. that they.The essence of the proposition that we rely on in describing the internal features of a given class of propositions. In logic it is only the latter that expresses: but that means that logic is not a ﬁeld in which we express what we wish with the help of signs. one might say. It is to get us to see how the propositions of logic ride on the back of the genuine propositions and thus have no status apart from the latter. We said that in the symbols which we use something is arbitrary.
To say that logical propositions presuppose that names have meaning and that elementary propositions have sense is again to emphasize the primacy of a notation. This feeling reﬂects the recognition that the propositions of logic do not stand on their own. Wittgenstein is ultimately concerned to claim that the very attempt to engage in this sort of formalization is an indication of a deep confusion. The logical proposition indeed reﬂects something about language and the world.1223). the Tractatus’ account of the propositions of logic as tautologies is meant to do more than suggest that (what this text takes to be) the standard approach to logic – the Frege/Russell formalization of logical inference by means of axioms and so-called rules of inference – is merely uninteresting or superﬂuous. The connection of logic with the world is preserved.

Wittgenstein announces his rejection of any justiﬁcatory use of inference rules. an underlying structure. remarking that they “are senseless (sinnlos) and would be superﬂuous. goes on: “One could therefore say the real name is that which all symbols. which signify an object. Carroll shows how the demand for a justiﬁcation for the inference from “p” and “p q” to “q” seems to require adding “(p & (p q)) q” as an additional premise in the inference. Once more it is evident that this “real name” is really no name at all:40 Wittgenstein’s account of the propositions of logic as tautologies is meant to show that the “entity” sought by the logician (that which is common to all the symbols) is ultimately nothing but a view of an entire linguistic system. Here Wittgenstein speciﬁcally has in mind the notion of a “rule of inference” as it functions in the formal logic of Frege and Russell.3411). The apparent need for such inference rules can easily be taken to imply that logic is concerned essentially to articulate the underlying relations between propositions – as if these rules provided the necessary justiﬁcation for the transition from one proposition to another. at 5.” rather than allowing the signs to “speak for themselves. The above-quoted reference to the proposition of logic as “a modus ponens represented in signs” is meant to drive home very much the same idea.1s referred to as the symbol’s ‘logical properties’] is that which all symbols which can fulﬁll the same purpose have in common” (TLP 3. Now earlier.341). how an understanding of logical inference is really only a matter of looking at the symbolism in the right way.Wittgenstein’s Tractatus understands to be the real motivation for such an enterprise is implicit in the above passage: it is the desire for us to specify the “nature of the absolutely necessary signs.” How are we to understand such a desire? For Wittgenstein the point would seem to be. have in common” (TLP 3. on the Tractatus’ account the logician imagines that in setting forth his formal language he has in fact laid bare that essential structure. the connection between this new premise and
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. but by the same reasoning. corresponding to what is necessary in the sign. that the philosophical logician imagines there to be a subject matter.” His position is thus often likened to Lewis Carroll’s in his famous article about the “paradox” surrounding modus ponens.132. as we recall. as always. Wittgenstein is then suggesting how misleading is this notion of an underlying logical structure. After remarking that “the essential in a symbol [what is in the 6. In saying that the signs must speak for themselves.39 One is reminded here of 3.3411. Wittgenstein.

” unformalizable character to logical inference. which expresses what is common to them. For the Tractatus. But while Carroll’s argument may well lead us to conclude that there is some special sort of “immediate. requiring a further premise. rather. there is a connection between their views. The confusion the Tractatus sees reﬂected in the logician’s reliance on inference rules betokens a reversal of this priority. just
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. I suggest.41 Certainly. “q” follows from “p” and “p q” in the ﬁrst place.” That is. we are to see this string of signs as a sinnlos symbol that represents internal features of a class of propositions. As always. for example.42 This explains why he ends 6. as it were. is primarily concerned to shift our perspective so that we no longer feel any urge to account for why.The essence of the proposition the original ones would also stand in need of justiﬁcation.1264 with the parenthetical remark: “And the modus ponens [which every proposition of logic represents] cannot be expressed by a proposition. what he is trying to say here is expressed simply in our willingness to count these particular propositions as exemplifying a certain form. which then must itself be linked to the previous ones. Wittgenstein is suggesting that. insofar as Wittgenstein and Carroll are both concerned to draw our attention to the special status of rules of inference. Since those common features are what we ordinarily refer to as inferential relations. Rules of inference thus really constitute nothing more than a misguided attempt to specify a priori the range of certain variables – which is to say that Wittgenstein’s criticism here has much the same form as his earlier criticism of the theory of types. as an instance of that tautology. the Tractatus. that through his rules of inference he is giving a priori license to certain inference patterns. Wittgenstein holds that we should understand “(p & (p q)) q” as a tautology. The logician imagines that he is in the position of legislating to language. logic for Wittgenstein comes in after the fact. and so on in inﬁnite regress. it is because they share those features that they are said to belong to the class of tautologies. every proposition of logic can then be said to constitute a “modus ponens” (in an extended sense of the term) – a means of reﬂecting the space of logical relations that already are taken to obtain. But that should make apparent that there can be no question of justiﬁcation or explanation in this context: it is not because some given set of propositions is a tautology that we say they have certain features in common but. as a way of describing an already given expanse of signiﬁcant utterances. though.

e.4661:
Now it appears to be possible to give the most general form of proposition (die allgemeinste Satzform). constructed). as constituting what is essential to the proposition. which falls under the description.
V
We now can begin to see how these considerations tie in with Wittgenstein’s remarks about the general form of the proposition. For this reason.. It is thus a kind of generalization of the tautology. Wittgenstein
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. The general form of the proposition. to give a description of the propositions of some one sign language. It is clear that in the description of the most general form of proposition only what is essential to it may be described – otherwise it would not be the most general form. i. if the meanings (Bedeutungen) of the names are chosen accordingly.46–4. then. can then be seen as a presentation of what is common to all propositions whatsoever. giving us in the most abstract terms possible just the proposition’s way of “representing” (again in the Tractarian sense of the term) the world.e. The latter notion is evidently meant to have tremendous signiﬁcance in the Tractatus: it is given extensive treatment through the 5s and indeed constitutes the subject of one of the seven principle remarks of the book – remark 6. in the way we operate with a set of propositions of this form.5)
As we have seen. that the concept of the general form of the proposition is ﬁrst introduced following the Tractatus’ initial discussion of tautology at 4.. We note. so that every possible sense can be expressed by a symbol. That there is a general form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i. The general form of proposition is: Such and such is the case. the tautology (or contradiction) is for Wittgenstein a means of showing what is common to certain classes of propositions and thereby of characterizing various internal features of language and the world. the logical connection between the premises “p” and “p q” and the conclusion “q” can only be shown – everything the philosopher would want to state here comes out in how we speak.Wittgenstein’s Tractatus like the sort of type restrictions that Russell attempts to institute. (TLP 4. and so that every symbol which falls under the description can express a sense.

43 If we can then specify in general all the methods of projecting the picture on to reality. from what allows it to present the existence and nonexistence of atomic facts. in 4. according to the Tractatus’ way of using the term. Since Wittgenstein in fact insists on the singleness of the logical coordinate system through which that projection occurs. is always a picture of the world.53 explicitly states. we recall that the original connection between the picture and reality is. Thus. this is just to say that the identiﬁcation of the general form of the proposition necessitates ignoring the speciﬁc logical forms of the propositions that are characterized. this very story helps to make evident the emptiness of the sort of summing up of the nature of logic allowed for by the Tractatus. for Wittgenstein. Wittgenstein says that all the symbols making up that
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. Given this background of a common form. therefore the essence of the world” (TLP 5. that is. Still. we will have described what is common to all states of affairs whatsoever – the essence of the world. But then the expression of the general form of the proposition must be a (high level) variable.4711). as 4. such a complete a priori characterization of the methods of representation should then be available. In more linguistic terms. For we note at once that this a priori account of representation can only be given by abstracting away from the form of the picture.44 At the same time.The essence of the proposition equates this general form with “the one logical constant” (TLP 5. the passage quoted above. of the existent and nonexistent atomic facts that the picture “presents. if it is important to see that the possibility of specifying the general form of the proposition is continuous with the account of logic as tautologous.5.47) and holds that its speciﬁcation is “the essence of all description. bringing to the fore what is common to properties of the symbol. But that means that what the picture represents – the speciﬁc determination of reality that is thereby made – will always be a state of affairs that could obtain. it is also important to be clear on how this possibility initially emerges out of the discussion of the picture.” The picture is then said to “represent” one possibility of its projection on to those states of affairs and thus a kind of choice within the ﬁeld of what it presents. secured by the identity of their pictorial forms – which is to say by the fact that a picture. the necessity of its being given all at once and in its entirety. Once more. we can speak of all the states of affairs that a picture can be used to depict. And that is precisely what is given by his speciﬁcation of the general form of the proposition. then.

55) The enumeration of any special forms would be entirely arbitrary. as Fogelin implies. The logical forms.554) 114
. as we have seen. is here once more giving expression to the thought that animates the whole Tractatus: namely.46 meant to communicate a signiﬁcant result. In this regard. that to the extent that we can gain clarity about the nature of our real aim in logic and philosophy. This point is in fact reafﬁrmed several times toward the end of the 5s:
We must now answer a priori the question as to all possible forms of the elementary propositions. The possibility of giving some sort of speciﬁcation of the logical forms – that is. of any attempt to specify a priori the limits of thought and language.Wittgenstein’s Tractatus expression are guaranteed to have a sense. in other words. as it stands. the expression for the general propositional form can be no more than a possibility for a proposition. Wittgenstein. we cannot give the composition of the elementary propositions. this suggests that. as long as “the meanings of the names are chosen accordingly.” Since it is only when the names in a linguistic string actually designate meanings (i. logical forms) that a genuine proposition is given. lies behind the “argument for simples” in the opening section of the text). the above mentioned distinction between “general form” and “logical form” is crucial. Since we cannot give the number of names with different meanings.e. as we have seen. The elementary proposition consists of names. we will see that this aim has lost its allure. (TLP 5. in the transparent vacuity of this culminating statement we are meant to see the vacuity of the Frege/Russell logic.. that such a speciﬁcation could only emerge through a consideration of the proposition as it is used (of what I mean in some context) – it cannot be given in advance. a kind of bare container in which a content is to be placed. Rather.47 We must be clear on how this deﬂationary view of the task of philosophy is also connected with the previously discussed notion of logical analysis.45 Wittgenstein’s paraphrase of the general form of the proposition as “Such and such is the case” is thus not. We saw from the discussion in the 3s. (TLP 5. are equated with the meanings of the names of the elementary propositions. the acknowledgment that the possible ascriptions that may be made to reality cannot await our discovery (the same thought that. the possibility of a complete analysis into elementary propositions – is secured by what Wittgenstein calls the deﬁniteness of sense. however.

As Wittgenstein puts the point at 5. the general form of the proposition. Nonetheless. the possibility of such an analysis is crucial. First.” We have seen that. the “what” – the content of our language – is not given independently of the logical scaffolding. in this sense logic precedes every experience. the imagined results of this analysis ﬁgure in Wittgenstein’s summing up of that which can be stated in advance – namely. given.557) If I cannot give elementary propositions a priori then it must lead to obvious nonsense to try to give them. Second. for the Tractatus. What lies in its application logic cannot anticipate. And how would it be possible that I should have to deal with forms in logic which I can invent: but I must have to deal with that which makes it possible for me to invent them. reﬂection on what it would have to entail is important in revealing the emptiness of the philosopher’s attempt to get at the fundamental categories of thought and language – the speciﬁcation of what the world. not before the What.552: “Logic precedes every experience – that something is so. For. that the notion of a complete analysis ultimately serves as a kind of thought experiment for gaining clarity about the technical logic developed by Frege and Russell. to be able to present the domain of the a priori in its entirety.” as Wittgenstein understands it in the Tractatus. But at the same time. for bringing out how the possibility of the latter rests on our already having a handle on the meaningful content of our language. (TLP 5. we can build symbols according to a system. (TLP 5. Where. then. The application (Anwendung) of logic decides what elementary propositions there are. Only that which we ourselves construct can we foresee. Wittgenstein is suggesting
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. It is before the How. the more technical presentation of that general propositional form involves conceiving of all propositions as truth functions of the elementary propositions. at its core.The essence of the proposition
It is clear that we have a concept of the elementary proposition apart from its special logical form. we must be able to conceive of the fundamental logical forms as. must be like. (TLP 5.555) There cannot be a hierarchy of the forms of the elementary propositions. in some sense. as we have seen. there this system is the logically important thing and not the single symbols. however.5571)
The actual carrying out of the analysis into elementary propositions is thus not itself part of “logic.48 One might say. as we shall discuss in some detail in a moment.

the Tractatus would in the end appear to present a quite Kantian49 view of logic as a condition of the possibility of all experience. of the Tractarian analogue to Kant’s transcendental theorizing? Kant. by presenting a proposition as the result of an
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. But why would that entail the emptiness of the speciﬁcation of logic – that is. and thus to conclude this part of our discussion of the Tractatus. at this point be at once apparent: his central idea is that the very possibility of formal expression of the general form of the proposition itself shows the emptiness of his “transcendental philosophy. Indeed. How it is that [(i. p. our manner of projecting our linguistic forms on to reality. Wittgenstein would seem to have done Kant one better. While it may be granted that it challenges the Frege/Russell picture of a determinate logical content. is required – thus logic can be said to determine only “how” the world is represented.”50 Nonetheless. Now the general direction of (what I claim to be) Wittgenstein’s response should. I hope. draws no such a conclusion about the status of his own work. one might well wonder just how “deﬂationary” Wittgenstein’s conception of this whole enterprise really is. as it points to the need for understanding in more detail Wittgenstein’s formal speciﬁcation of the general propositional form. his real point is then that the formalisms of Frege and Russell constitute no more than an account of our way of constructing the proposition.21: “We can bring out these internal relations [between the structures of propositions] in our manner of expression. I do not view the above as a mere straw man objection. Or so one might argue. we hardly seem to be left with nothing to replace that picture. Nonetheless. but it ultimately does not constitute a complete undermining of their respective enterprises. On the contrary. as the above passage suggests.Wittgenstein’s Tractatus that logic has no life apart from the sensical expanse with which we are presented. This term is introduced at 5. The Tractatus’ conclusion may be a step back from the metaphysical excesses of Frege and Russell. a prior given. a “what” on which to operate. .e. just as with Kant’s transcendental conditions of knowledge (the forms of the intuition and the categories of the understanding). To be sure. since his version of transcendental logic is apparently capable of precise. N( ))] is meant to ¯ say no more than “Such and such is the case”? To answer this question. after all. purely formal expression. we must ﬁrst consider Wittgenstein’s notion of an operation.

the operation will describe a common feature of a class of symbols – thus Wittgenstein says that it brings out internal relations between the structures of propositions. logical multiplication. he expressly holds above that that sense is reversed by negation. as we have seen. As giving prominence to the representing dimension of the picture. Negation.52
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. as always in the Tractatus. are operations. what he is saying. what is said here about the operation should then not come as a surprise. expressed by means of a variable (this is explicitly stated of the operation at 5.2522). he insists that the notions of operation and function must not be confused with one another (TLP 5. it does not touch the internal make-up of the proposition. the function cannot be its own argument (“x is a table is a table” does not characterize any class of propositions). logical addition. is that logic assumes a pregiven content in a certain sense. as 5.) Similarly. as an operation. the symbol – and the operation – the reworking of the truthfunction – are. etc. while the operation can take one of its own results as its base ( p can again be denied). that. Hence.2341)
The operation is. (TLP 5.25): this is just to reiterate the point that the expression of a common feature of a class of symbols will abstract from the logical forms of the propositions characterized. for Wittgenstein. (TLP 5. Wittgenstein’s formal means of handling the truth functional connectives. he remarks that “the occurrence of an operation does not characterize the sense of a proposition” (TLP 5.) (TLP 5.234) The sense of a truth-function of p is a function of the sense of p. (These operations I call truthoperations. Given our previous discussion of the Tractatus’ treatment of this issue.The essence of the proposition operation which produced it from other propositions (the bases of the operation). after all.232) Truth-functions of elementary propositions are results of operations with elementary propositions as bases. in the ﬁrst instance. they stand. too. etc. For the same reason.25).” He then continues:
The internal relation which orders a series [of forms] is equivalent to the operation by which one term arises from another. (Negation reverses the sense of a proposition). Although both the propositional function – that is. Instead. at different levels.24 and 5.251 emphasizes. that the logical constants are only applied to propositions already having a sense.51 (Wittgenstein is of course not here asserting that the truth-operations have no effect whatsoever on the sense of a proposition.

For what Wittgenstein is here seeking
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. Conﬁning ourselves for the time being to the context of truth functional logic. a schema for one or more propositions. Wittgenstein can hold that he has characterized the whole of truth-functional logic: since the Sheffer stroke constitutes a truth-functionally complete set. In this way. O’O’a. N ζ)] – then provides ¯ for the possibility of making such selections from the set of all elementary propositions. it constitutes a generalized version of the Sheffer stroke of joint denial.” and so on.” i. there is a question about how exactly to understand the functioning of the “ζ” notation. however.” “N(p. O’a. is a Tractarian variable. for the Tractatus.” “N(N(p.2522:
The general term of the formal series a.
This makes it evident that. . x.” it is clear. we must ﬁrst understand the particular operation he is concerned to deﬁne – “N(ζ). every nonquantiﬁcationally complex sentence would appear somewhere in the formal series generated by iterated applications of the N operator to the elementary propositions. To see how Wittgenstein will make use of such a speciﬁcation. the second the form of an arbitrary term x of the series. O’x]. “x” the nth step in the development of the series. Just this need for iterated applications of operator N is key in assessing the import of this approach. we can for the moment ignore it and simply follow Wittgenstein’s instructions at 5. and the third the form of that term of the series which immediately follows x. the characterization by means of an operation involves a recursive speciﬁcation: in the variable contained in the brackets. it is not difﬁcult to see what Wittgenstein has in mind. . As we shall soon see.502). I write thus: “[a.” This expression in brackets is a variable. .e.501 to take the “ζ” as standing for all the values of a given variable. “N(ζ)” is then to be understood as “the negation of all the values of the propositional variable ” (TLP 5. But as that question becomes most relevant in connection with the account of quantiﬁcation.Wittgenstein’s Tractatus Wittgenstein gives his more formal presentation of the notion of an operation at 5. The ﬁrst term of the expression is the beginning of the formal series. q))” yields “ ( p & q) & ( p & q). ζ. “p v q.” “ . q)” yields “ p & q. For example. “a” represents the basis step. substituting “p” and “q” (which can stand for either elementary or nonelementary sentences) for “ . and “O’x” (the application of the operation to the nth step) the nth 1 step. The variable represented at 6-[(p.

The essence of the proposition to bring out is what has been implicit throughout the Tractatus – namely, that any systematic presentation of logic must rely on the “etc.,” the “and so on.”53 Indeed, he expressly remarks: “The concept of the successive application of an operation is equivalent to the concept ‘and so on’ ” (TLP 5.2523).54 The point, in other words, is that the “givenness” of the whole of logical space – that is, of that which the picture was said to “present” – is ultimately just the possibility of our always being able to go on, to continue a pattern. Certainly, our ability to identify such a pattern is important, in that it allows for the possibility of, as Wittgenstein puts it in the Notebooks, “constructing logic and mathematics . . . 55 from the fundamental laws and primitive signs” (NB 89). (Conversely, we might note, precisely the absence of this sort of pattern precludes an a priori speciﬁcation of the forms of the elementary propositions; one could say that there is simply no explanation of why it is nonsense to speak of the weight of a noise.)56 But the force of Wittgenstein’s own characterization of the general form of the proposition is to make apparent that logic is no more than that – that, in the end, the domain of the a priori is nothing but the possibility57 of repeated applications of a rule. Still, even if we accept this as an interpretation of Wittgenstein’s analysis of truth functional logic, it is not at once apparent how this same sort of treatment could be extended to quantiﬁcational formulas. For consider how generality is expressed in the notation supplied by the Tractatus. As that notation includes no sign for the quantiﬁer, Wittgenstein must rely on the possibility of applying the N operator to a potentially inﬁnite number of propositional arguments. Thus 5.52 reads: “If the values of are the total values of a function fx for all (∃x)fx” (TLP 5.52). In other words, if the values of x, then N( ) values of the function “fx” are the propositions “fa,” “fb,” “fc,” . . . then “N(fx)” is equivalent to the joint denial of all those propositions, that is, to “ fa & fb & fc, . . . ,” an expression that is equivalent to “∀x fx.” A further application of N would then yield the formula “∃xfx,” and so on. In this way, Wittgenstein’s N operator is capable of handling generality58 and in a manner that is seemingly consistent with his truth-operational understanding of the proposition. The central question that this approach raises, however, concerns the original speciﬁcation of the values of the variable to which N is applied.59 For what does it mean to say that a propositional variable “gives us” a set of values? If the notion of an operation is needed to
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Wittgenstein’s Tractatus clarify the givenness that belongs to the inﬁnite expanse of logical space, how can the givenness of a potentially inﬁnite set of propositions be here treated as unproblematic? Moreover, such a view would commit Wittgenstein to understanding generality in terms of logical sum or product: to treat the variable as a name for a very lengthy list of propositional values is just to take a universally quantiﬁed statement as nothing but a (possibly inﬁnitely) long conjunction. But the Tractatus asserts that the concept “all” must be “disassociated from” the truth-functions and explicitly criticizes Frege and Russell for “introduc[ing] generality in connexion with the logical product or the logical sum” (TLP 5.521). One might suppose these difﬁculties can be circumvented by supposing that, since a variable is understood as an indication of a type of proposition, it is imagined somehow to specify its values as a set, as a kind of totality. Wittgenstein’s point would then be that in denying this variable we simultaneously deny all its values, without having to enumerate these one by one.60 This could seem to be why he distinguishes generality from logical sum or product. While this interpretation is not altogether incorrect (as we shall see), the problem is that in requiring that the N operator be applied directly to the propositional variable in this way, we run up against the earlier claim prohibiting the operation from characterizing a sense. For N in this case effectively serves as a quantiﬁer binding a free variable and thus would now be responsible for turning an open sentence into a genuine proposition. Wittgenstein’s understanding of generality cannot then involve such an approach. To see what he has in mind instead, we ﬁrst must look at 5.522: “That which is peculiar to the ‘symbolism for generality’ is, ﬁrstly, that it refers to a logical proto-picture (logisches Urbild; Ogden “prototype”), and secondly that it makes constants prominent.” This rather dark remark becomes helpful when read in connection with Wittgenstein’s earlier discussion of analysis. We thus recall his discussion of the complex at 3.24 and its connection with the account of the vagueness of the ordinary (unanalyzed) proposition. Rather than viewing the complex as a special kind of object on whose existence the meaningfulness of certain propositions depends, the Tractatus, as we saw, understands this notion linguistically – that is, as one or more logical forms or proto-pictures that have been contracted into an apparent name via deﬁnition. The proto-picture here functions as a means of leaving room for the things in the world to have a range of,
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The essence of the proposition say, color values, without our having to specify which value must be assumed. The complexity of the world is in this way reﬂected in a certain indeterminateness in the unanalyzed proposition. But then since the discussion at this point is intimately connected with generality (we recall 3.24’s remark – echoing 5.522 – about how the “notation for generality contains a proto-picture”), it appears that it is precisely through this indeterminateness that we gain our understanding of the quantiﬁer. Generality, in other words, is to be equated with the propositional constituent seen as a representative of an arbitrary location within a particular logical form. What this discussion ﬁrst makes apparent is that generality for Wittgenstein ﬁnds its natural home within the context of the signiﬁcant (unanalyzed) proposition. After all, we saw earlier that the indeterminateness that marks the appearance of the logical proto-picture is understood as making possible just the deﬁniteness of sense. In remarking that the symbolism for generality refers to a logical protopicture, Wittgenstein is then not faced with Russell’s problem about the status of an asserted propositional function.61 He is not, in other words, led into viewing such a function as a genuine, self-standing proposition with a special sort of ambiguous sense. For him, instead, the application of the proto-picture is given just by its contribution to the sense of the proposition in which it occurs; generality, we might say, is absorbed into our means of representing the particularities of the world. Still, even if Wittgenstein’s account is not saddled with the notion of a propositional function as a self-standing assertion, one might still wonder if his reliance on the idea of a representative of an arbitrary formal place is any clearer than Russell’s “ambiguous denoting.” Here it becomes important to consider the above remark about the prominence of constants in the notation for generality. Now one might suppose that by “constants” Wittgenstein is thinking of “names” as opposed to “functions,” but in fact at 3.312 he uses the term in almost the opposite sense: “[An expression] is therefore represented by the general form of the propositions which it characterizes. And in this form the expression is constant and everything else variable.” With this in mind, his point would then seem to be that generality brings into prominence what is common to a class of propositions, and that it does so precisely by taking certain parts of these propositions to be “variable,” arbitrary. For Wittgenstein, then, the possibility of speaking
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which. while I cannot list all the possible locations. .) The potentially inﬁnite set of propositional values that is “given” by a Tractarian variable is here really just the possibility of placing the watch in any location allowed for by this particular form. To illustrate. but let us focus on the latter. .63 still I do not happen on a place for this watch that I did not anticipate. In terms of the picture theory. that I do not discover the sense of my utterances. where the bar notation is introduced:
An expression in brackets whose terms are propositions I indicate – if the order of the terms in the bracket is indifferent – by a sign of the 122
. both the concept “watch” and the concept “on the table” are understood as here presenting implicit generalizations.” Let us look more closely at 5.Wittgenstein’s Tractatus of “all” assumes not the existence of a kind of indeﬁnite entity. How is the generality in the notion of something’s being on the table to be expressed? Wittgenstein would suggest that it is evident precisely in the fact that I can understand this as saying “φ is at location a or φ is at b or φ is at c.501. but a way of gesturing toward a symbol. it seems. ignore the picture’s internal makeup and concern only its projection as a whole.” The “and so on” here does not denote the “dots of laziness”. We now can begin to make better sense of the Tractatus’ formal way of handling generality. as in the case of the truth operations. it is not as if my sentence constitutes an abbreviation for a lengthy disjunction that I really intend. and so on. It is by reﬂection on this idea that we begin to see the key to Wittgenstein’s view of generality: the arbitrariness that is essential to a generalization is. the possibility of continuing this series is given just by a logico-pictorial form. Rather. equivalent just to the possibility of constructing a picture of a particular form. the interpretation of “ . (Recall once more Wittgenstein’s insistence that I know what I mean.62 In this way the quantiﬁer is distinguished (“disassociated”) from the truth functions. a feature of the proposition that helps characterize its sense. This requires that we return to the difﬁculty that we earlier passed over – namely. But neither does that sentence present me with a rule for continuing this formal series. To understand the form “on the table” is to see it as permitting this location or this location or . let us revert to our earlier example of the assertion “The watch is on the table. . as we have seen. to that which makes it into a picture in the ﬁrst place. we could say that generality requires us to pay attention to the internal structure of the picture – that is.” For the Tractatus.

as we suggested above. again. precisely through the possibility of our going on with the series “fa. . as Fogelin. . It is then true. however.521 insists that generality must not be introduced in connection with logical sum or product.” For the Tractatus.” “fc.” By means of the bar notation we are presented with the series of “fx’s” values – “fa. – and it is to those values that N is directly applied.67 It now becomes clear how we are to understand the application of the N operator to a propositional function “fx. .. 5. .
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.The essence of the proposition
form “(ζ).” “ ” is a variable whose values are the terms of the expression in brackets. fc. . the ellipsis here represents just our capacity to designate any arbitrary sentence of this particular form (whatever form the variable schema “fx” is standing in for in some propositional context). appears to hold.” . . and the line over the variable indicates that it is the representative of (vertritt) all its values in the brackets.” “fb.” Wouldn’t “ ” be “representative of all its values” – would it not demarcate a whole class of propositions – before the bar has been added? We must then look at this issue in light of the above discussion. fb.66 Wittgenstein’s notation thus bring out how the possibility of a generalization does not require the occurrence of a free variable. .” in other words. that the result of this operation can be represented as “ fa & fb & fc. Given what we have seen to be Wittgenstein’s understanding of generality. how it involves only a means of alluding to a series of propositions of a given form. . for example. I suggest. it would appear that what is in fact needed is to add to the expression of a propositional variable a means of specifying some arbitrary member or members of the class of propositions that it describes.” Given the possibility of unlimited applications of the N operator – as well as some means of marking scope distinctions – we can then in the same way generate every sentence of ﬁrst-order logic. is precisely the function of the bar notation: to place the bar over “ ” is to allow for the possibility of this variable64 standing in for65 some one or more of its values. since a variable for Wittgenstein serves to characterize a particular class of propositions (a point that is reiterated at 5. that the application of N requires us actually to complete a (possibly inﬁnitely) long enumeration. it is not at once obvious what is the difference between “ ” and “ .”68 This is not meant to imply.501). This.. we could say that the grammar of “inﬁnite list” is entirely different from that of “enumeration. We arrive at the generalization “∀x fx.
The problem here is that. then. in the terms of the later Wittgenstein.69 For.

which . The Tractatus’ presentation of the general propositional form tells us that we know how to construct truth functions and sentences of unlimited quantiﬁcational complexity. i.
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. the generalization does not constitute a special kind of representation of the world. To acknowledge that as the answer to the fundamental question of the philosophical or logical inquiry would seem to be to acknowledge the hollowness at that inquiry’s heart.”: and this x is a. . But that.Wittgenstein’s Tractatus The Tractatus thus can succeed in its task of showing how every proposition is the result of truth-operations on the elementary propositions. This may seem unsettling: one feels as if Wittgenstein’s speciﬁcation of the general form of the proposition has not truly gathered together. that is what it is to say that we can give in advance no more than a method for representing the world. the possibility of forming general propositions rests once more on the possibility of continuing a pattern. all the signiﬁcant propositions – that we. ineliminable role in the Tractatus’ account. are only shown what it would mean to make a signiﬁcant utterance in some given case. at best. Wittgenstein suggests that it is with this answer that we must rest. of course.526 emphasizes the potential equivalence of a purely generalized description to description by means of names: “One can describe the world completely by completely generalized propositions. without from the outset co-ordinating any name with a deﬁnite object. In order then to arrive at the customary way of expression we need simply say after an expression “there is one and only one x.e. but simply a different way of applying a symbol.” Rather than requiring the existence of special sorts of general facts. On this account. The notion of continuing a pattern thus plays a central. 5. . is just the point. Thus. as it were.

we would do well to review where we have been. Instead. let alone as a further fact about the world. if. a certain oddness in speaking here of a “conclusion. it is just a particular way of looking at what is the case: the revealing of the form of the object turns out to involve nothing more than a description of the world that will make perspicuous the combinatorial capacities of that description’s
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. cannot be conceived as a self-standing entity. There is. as we have held throughout. seeking to adopt a “logical” perspective on the world. should we not suppose that everything of importance has already been said? Still. a genuine understanding of the views of Wittgenstein can only be conveyed through a detailed appreciation of the movement of his thought. one wonders about the status of any summary remarks that we might have to offer. We recall.CHAPTER IV
THE LIBERATING WORD
I
Having completed our study of the details of the Tractatus. This involves the attempt to specify the real nature – the form – of the objects conditioning what is the case. How can it be that the Tractatus’ real purpose is an ethical one. to be sure. the question of how the author understands the ultimate outcome of his endeavor remains to be directly addressed. then. the perspective from which the possibility of the facts is revealed. We saw that this form. we can now reconsider from a more general perspective its fundamental aim or aims. After all. from the beginning. as given by the full range of the object’s occurrences in a space of atomic facts. as Wittgenstein suggests? Before approaching the question. that this text can be understood as.” given what has been maintained thus far about the nature of this text.

We saw. only shown. is just to express the emptiness of the question motivating this whole inquiry. While this move already shifts our understanding of the philosophical or logical inquiry. then. that logical analysis is required to reveal what my assertion really says. however. but this possibility. But since for the Tractatus having a variable entails already being given its (propositional) values. the assertion of deﬁniteness of sense is equivalent to the denial of the possibility that I could discover what I mean. the proposition is viewed as having a deﬁnite sense that it is the task of analysis to bring to light. for Wittgenstein. The initial discussion of the picture brings us to see that any insight into the possibility of constructing a picture that can depict the world is parasitic on an understanding of the nonarbitrary aspect of the correlation of pictorial elements and their real-world counterparts (the analogue in this context to the form of the object). While. according to Wittgenstein. how the “picture theory” reinterprets that inquiry’s central question as the demand for an a priori speciﬁcation of the possibility of the positive/negative fact. Analysis will then involve the attempt to delineate the occurrence of those variables and thereby make perspicuous the meanings (Bedeutungen) of the names. To say that.Wittgenstein’s Tractatus fundamental components. what the Tractatus calls the picture’s pictorial form (Form der Abbildung). it is to suggest that everything philosophy would want to say about the essence of representation emerges only through the application of the picture to the world. We then saw how the treatment of picturing is extended to the notion of the proposition via the Tractatus’ concepts of logical form and analysis. That such a correlation has been effected is assured simply by virtue of a particular fact’s being a picture. the real force of the Tractatus’ claims here only begins to become apparent in the discussion of the picture. The meanings of the names emerge in what is common to that class – which implies that those meanings are
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. it became apparent that this is not to be understood as an application to ordinary language of a Fregean refusal to countenance vague predicates. The ordinary proposition stands in perfect logical order and can do so precisely because it implicitly makes use of “proto-pictures” – that is. the variable’s “delineation” comes to no more than the speciﬁcation of a particular class of propositions. Rather. cannot itself be represented. variables – that enable us to allow for a certain indeterminateness in our utterances.

The logical forms. are to be construed simply as ways of characterizing the already given expanse of signiﬁcant utterances. of going on in the same way. “presents” (vorstellen) all those states of affairs (both existent and nonexistent) it can be used to depict. What reﬂection on the idea of analysis thus makes clear is that. we can speak of what is common to any manner of representing the world whatsoever. Thus. on the one hand. for Wittgenstein.
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. On the other hand. however. this complete a priori characterization of the nature of depiction is summed up by Wittgenstein’s generalized version of the Sheffer stroke. just as in the case of the picture and its form of representation. Wittgenstein thus introduces his view of the logical constants as the speciﬁc methods by which the pictorial fact can be projected on to reality. it merely points us toward the possibility of continuing a pattern. but just a way of viewing how we in fact speak. we explored how the picture theory also underlies Wittgenstein’s treatment of the logic of Russell’s Principia Mathematica and Frege’s Begriffsschrift and Grundgesetze. But since. The picture. how this presentation of the general form of the proposition relies on an ineliminable use of the ellipsis and thus does not constitute a genuine deﬁnition. A kind of generalization of the tautology. philosophy’s proper concern – the possibility of making sense – is not a self-subsistent domain conditioning thought and language. we are meant to see that the formalisms of the Begriffsschrift and the Principia serve only to reﬂect the hollow casing in which the signiﬁcant proposition is to be placed. In Chapter III. and hence as a way of characterizing (what we would ordinarily think of as) inferential connections between propositions. it must also be possible to give the “general form” of the proposition. but logical forms. We saw that the tautology (or contradiction) can be conceived as a means of bringing to the fore what is common to the speciﬁc methods of projection of a class of sentences. his operator N.The liberating word not things or entities in the ordinary sense. Far from dictating to thought its fundamental laws. the Tractatus’ complete a priori characterization actually brings out the emptiness of the Fregean and Russellian view of logical inference. We saw. it “represents” (darstellen) a particular state of affairs within that determinate space. in turn. Instead.

that we grasp how to extend the kind of point the Tractatus makes to any (arbitrary) philosophical “problem” that should happen to grip us. For the Tractatus to claim to have exposed the emptiness of philosophy tout court. Of course. say.” And indeed. Now. as we have just noted. on reﬂection we realize that it would be contrary to the Tractatus’ fundamental stance – its eschewal of general criteria of sense and nonsense. through a clariﬁcation of the essence of those confusions. as we have emphasized.1 while every nonsense utterance is nonsensical in its own way. that is. After all. we must be able to go on in the same way with the inquiry represented in the text. how the simple possibility of following a rule lies at the heart of formal logic. its reliance on a dialectical methodology – to attempt to provide any such general description of the pseudo-proposition. This difference is evident in the absence of any speciﬁcation for the nonsensical pseudo-proposition corresponding to the “general form” of the (signiﬁcant) proposition – in the absence. Instead. of our grasp of the generality of its application. this is largely a reformulation of the point emphasized throughout regarding the absence of genuine arguments in the Trac128
. This entails. one might say that for the Tractatus all signiﬁcant sentences are alike. in the Introduction to this study and at the end of the last chapter. of a systematic summing-up of what is common to all those utterances that Wittgenstein would describe as “nonsensical. That discussion brings out. To paraphrase Tolstoy. we suggested that Wittgenstein’s account must itself in a certain sense rely on our ability to continue a pattern that has been initiated. There is and can be no logic of nonsense.Wittgenstein’s Tractatus
II
The Tractatus’ discussion of the general form of the proposition is an appropriate place to begin our ﬁnal reﬂections on the overall purpose of Wittgenstein’s text. that we are able to understand such a problem as a confusion. Wittgenstein seeks to carry out this task in a wholesale manner. of formal and genuine concepts (to use just one of the formulations Wittgenstein employs). But now we must face up to an important dissimilarity between the role of the “and so on” in the characterization of the signiﬁcant proposition and its role in continuing the central philosophical task of the text as a whole. ultimately. the Tractatus does not attempt – nor could it attempt – to unravel one by one every confusion by which philosophy has been bedeviled.

It is in ethical terms that the inquiry of the Tractatus can be said to assume a unity. We are once more reminded of 6. what sense can there be in supposing that we might continue “in the same way” Wittgenstein’s endeavor? What is the endeavor we are to continue? One might be tempted to say that it is just on this dilemma that the early Wittgenstein’s whole inquiry founders. it would be a mistake to suppose that Wittgenstein in the Tractatus has no response whatsoever to the question we are raising. Instead. self-standing claims. or that certain features of the proposition can only be shown. One then thinks back again to the Preface and Wittgenstein’s remark that his book will only be understood by those who have had the same or similar Gedanken. the metaphysical impulse they aim to eliminate. the characterization of logical truths as tautologies. no interest whatsoever in simply “asserting” that a logical truth is a tautology. or as directed against. there can be no purpose. Over and over we have seen how Wittgenstein’s key claims – his remarks about the nature of objects and the distinction between Tatsache and Sachverhalte. the show/say distinction. these remarks serve their clariﬁcatory purpose – they become “nonsense” in the requisite sense – only when they are taken in connection with. the inability of Wittgenstein’s text to compel us to adopt its perspective on the nature of philosophy. I suggest that his response is quite connected with his understanding of the point of the text as ultimately ethical. how. For without the capacity to indicate the common component – or components – of the nonsensical pseudo-proposition. and so on – can only be understood as responses to certain philosophical questions. but now with a slightly different emphasis: he who understands
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. But while we have emphasized throughout how there is indeed a shift in his later thought toward the recognition of the multifariousness of philosophical inquiry. We may approach this issue by ﬁrst reminding ourselves of the peculiar character of the dialectic in which this text is engaged.The liberating word tatus. But now it appears as if this idea stands in fundamental tension with the text’s aim of silencing altogether the philosophical voice. The inseparability of Wittgenstein and his metaphysical interlocutor is at the heart of the Tractarian dialectic.54 as well. We have stressed how this recognition precludes our taking Wittgenstein’s remarks as general. indeed as the means of clarifying just what those questions are. for him.2 On the contrary.

5 The true insight into nonsense. the im130
. (They are of the same kind as the question whether the good is more or less identical than the beautiful. then. Instead. the Tractatus aims to deliver us to the world. Hence his oft-quoted remark:
Most propositions and questions that have been written about philosophical matters are not false but nonsensical. is to get us to see these demands as illegitimate. on language. (TLP 4. the genuinely philosophical “problem” only appears as such to one who places certain demands on the world. To be in the grip of philosophical perplexity. Consequently we cannot give any answer to questions of this kind. Wittgenstein’s aim. as an attempt to put our words to a task to which they are not suited.) And it is not surprising that the deepest problems are in fact not problems at all. in turn.Wittgenstein’s Tractatus me understands my propositions as nonsense. We might put matters as follows. really to engage in a double movement.4 Philosophical nonsense results not because of anything inherently unachievable but because of an ongoing conﬂict in our own desires and aims. however. for Wittgenstein. can then be nothing but a release from self-conﬂict. To grasp the propositions of the Tractatus is. who insists that our understanding must conform to this model.3 But then that is to say that the recognition of the nonsensicality of philosophy is. from this fundamental disharmony in our being. is not to be in a situation where one is incapable of ﬁnding a solution to a complex problem. to trivialize philosophical perplexity. always a recognition that we are at odds with ourselves. We are to acknowledge as illusion what we thought was our soughtafter end. We are to see in them the kind of thing we ourselves are aiming for and simultaneously to recognize that aim as not achievable. but can only point out that they are nonsensical.6 What the above remark refers to as the depth of philosophical (pseudo-) problems is taken seriously: for Wittgenstein. to sneer at those who are in its grip. Most questions and propositions of philosophers arise from our failure to understand the logic of our language. for Wittgenstein. In liberating us from the inner discord that deﬁnes the metaphysical impulse. his aim is to bring us to acknowledge that our expectations for a philosophical explanation are in the end only our expectations.003)
To say that the deepest problems are not problems at all is not. it would seem.

8 “even if all possible scientiﬁc questions are answered our problem is still not touched at all” (NB 51).372)
Wittgenstein claims that at the basis of the modern view is an “illusion. as providing a complete answer. in one respect. as Wittgenstein has aimed to bring out throughout the
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. whereas the modern system makes it appear as though everything were explained.371) So people stop short at natural laws as at something unassailable. But the ancients were clearer. But neither are we to turn to nonscientiﬁc modes of explanation. on his view. but for recognizing.The liberating word pulse toward philosophy arises out of a sense of profound rupture with the world. And they both are right and wrong. as did the ancients at God and Fate. that his philosophical task is ultimately one of limiting reason’s scope in this regard. They are right because. But we note that in the passage above it is held that. Of course. one that is apt to be experienced by anyone we should regard as serious. as he puts it in the Notebooks. that the pursuit of philosophy is to be replaced by a kind of scientism. for the Tractatus. but.” the appeal to God or fate is. an acknowledgment that there is a point at which nothing more can be said. however.” He is not suggesting. (TLP 6. the moderns are right in treating natural laws as unassailable. is just its tendency to misinterpret that feeling of disquiet. in so far as they recognized one clear terminus.10 What Wittgenstein considers as characteristic of the philosophical approach. it may now begin to sound as if Wittgenstein is claiming that there are in fact genuine questions that science or human reason can never answer.7 a sense that. that explanations come to an end somewhere: rather than serving as the basis of an ultimate “super account.9 Of course. This whole issue can be seen to underlie the following important remarks:
At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena. a belief that the deepest yearnings of human beings can ﬁnally be met in the context of scientiﬁc progress. in the words of the later Wittgenstein. The ancients are here commended not for having a superior explanatory system. then. (TLP 6. to misconstrue what is appropriate as a response. Our unease in the world crystallizes into unresolvable philosophical perplexity. this is a sense that is not peculiar to philosophers.

against supposing too readily that our fundamental questions have truly dissolved. Instead. Thus Wittgenstein intersperses remarks about the disappearance of philosophical problems with claims about the appropriate way of living in general: “The solution of the problem of life is seen in the vanishing of the problem. that is.521). We are to see.12
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. it is only when we face honestly our experience of our lives as problematic that we can hope to attain the sort of insight. how there is after all nothing for us to do to satisfy these kinds of concerns. however.Wittgenstein’s Tractatus Tractatus. as the attempt to set down a formal speciﬁcation of the laws of thought. In gaining clarity about our philosophical confusions we can then be said to be liberated from the problem of life.11 once more the deepest problems are held to be no problems at all. in the words of 5. logic must take care of itself. the sense that our fundamental relationship to the world is something that requires a straightforward solution. it is thus not a matter of placing a prohibition on reason’s ability to address certain kinds of questions. Over and over. about what we ultimately believe. And over and over we are to see in response how. For him. We must not mistake indifference or obtuseness for a genuine understanding of what Wittgenstein calls the “sense of life” (6.521). The real thrust of this passage. the text attempts to expose the different guises of philosophical disquietude: as the demand that the picture’s fundamental relation to the world be once and for all secured. as the need for a theory of types to prevent nonsense. Wittgenstein’s praise of the ancients. we might then say.473. is to suggest that an easy satisfaction with the results of science is the wrong kind of satisfaction. The Tractatus then seeks to get us to see how philosophical perplexities can be expressions – indeed the complete embodiment – of that fundamentally problematic relation to the world. We must not deceive ourselves about who we are. (Is not this the reason why those who have found after a long period of doubt that the sense of life became clear to them have then been unable to say what constituted that sense?)” (TLP 6. connotes an attempt to caution against arriving too quickly at this insight. outside of the scope of the sciences our purported explanations of the world are merely pseudo-accounts. the redemption that he envisions. how it is the concerns themselves that are the source of our fundamental unease. but rather of showing that those questions are not genuine questions in the ﬁrst place.

what we are now seeing more clearly is that the ascription of the string “nonsense” signals.” and so on) in a new manner. my very will that is at issue when I characterize philosophy – my own philosophical utterances – as nonsense. I will now see persistence in the activity of philosophizing as an indication that my will is at odds with reality. Wittgenstein might say.
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. thereof one must remain silent” (TLP 7) – as the mark not of logical necessity but of ethical obligation.16 that I am refusing to accept fully the course of my experience. But Wittgenstein assumes that once we have grasped the insight at the heart of this text such questions will no longer tempt us. My willingness to invoke this term carries with it the recognition not simply that some string of signs is illegitimate and must be withdrawn but. Wittgenstein seeks to change my whole way of viewing. a basic shift in our orientation toward the world. philosophy comes to stand for our fundamental estrangement from the world.” For while we can make straightforwardly meaningful judgments about the application of the latter. And that is to say that to “go on” with the task of the Tractatus is ultimately just to acknowledge the “must” in the text’s ﬁnal remark – “Whereof one cannot speak.The liberating word If.” “logic.15 But that is then to suggest that the possibility of “going on” with the Tractarian enterprise is misdescribed when it is as presented as the problem of determining the future applicability of the term “nonsense. it is then in the disappearance of philosophy that our redemption lies.13 We can now return to our question of how this text’s own remarks are to be generalized to all of philosophy.” “thing. for Wittgenstein.” Rather than aiming to bring me to use a word (or a whole set of words – “fact. my fundamental attitude toward. The above considerations have been intended to bring out more sharply the basis for our fundamental contention throughout that this text’s usage of the predicate “nonsense” cannot be assimilated to the ordinary usage of a predicate like “red. philosophy: I am now to see the philosophical activity as essentially an attempt to make impossible demands on language and the world. for the Tractatus.17 It will be taken as a sign that something has gone awry in my way of living.14 It is. that the impulse leading to the utterance of those signs is itself questionable. rather. This is not to deny that philosophical questions might arise for me after I have read – and understood – the Tractatus.

we too must continually attempt to wriggle free from their grip – silence in this circumstance would betoken no more than a refusal to acknowledge the reality of our own confusion. Are we now to view philosophy as a shameful activity. For with regard to the former. to close our study with an unequivocal endorsement of Wittgenstein’s practice and of philosophy generally. There are. he is involved in deepening his original insight.Wittgenstein’s Tractatus
III
Wittgenstein. Philosophy for us thus becomes not a ladder. and hence an endless process of philosophical clariﬁcation. This principle might thus seem to be worse than empty. For insofar as we too are forever being caught in the snare of philosophical perplexities. perhaps Wittgenstein may then be deemed innocent of the more serious charge of hypocrisy. as we have discussed. “Problems are solved (difﬁculties eliminated). The acceptance of this general picture seems to clear a space for our own continued involvement in philosophy as well. for besides not even binding its own author. endlessly various in their form. and quite egregiously: the rest of his life is spent speaking of those things of which we must remain silent. will seemingly violate his own ethical maxim. rather. it is undeniably the case that Wittgenstein’s later engagement in philosophy is something other than a mere repetition of his Tractarian views. and in so doing gives up the early governing idea of an essential confusion from which we can be essentially liberated. endless philosophical confusions. my engagement in it a sign of my corrupt character? Does Wittgenstein’s inability to resist its allure not mark him as one who lacks the courage of his own convictions? It is tempting here to strongly resist these conclusions. ascended once and then permanently cast aside. Such a shift would appear to go some way toward revoking the Tractatus’ requirement of a kind of absolute philosophical silence. not a single problem” (PI 133. In the Investigations’ vision of philosophy. emphasis Wittgenstein’s). for the later ﬁgure. then.
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.18 What Wittgenstein comes to see. of course. The Tractatus may then be reinterpreted as the means of starting us down this route and alerting us to many of its central features. is that the whole idea of philosophy as a “fundamental” impulse toward the world cannot be sustained. it serves to attach the stain of sin to philosophical inquiry. but a path of clariﬁcation.

nothing but illusion.” with all their attendant slipperiness. it would seem. Nor is this a mere idle possibility. For Wittgenstein. as the deeply metaphysical history of Tractarian scholarship might suggest. depends always on the possibility of bringing us to confront the core of the “problems of philosophy. After all. we are now (ﬁnally) in possession of an entirely reliable method of philosophizing – as if. at its heart. the nagging questions about the ultimate value of philosophical activity have once and for all been put to rest. of the dialectical approach it exempliﬁes? How stable is the state of ultimate clarity with which this text tantalizes us? If the Tractatus wants us to understand philosophy as. with Wittgenstein. Wittgenstein’s “method. we must temper the familiar impulse to suppose that. What does this mean for our understanding of the fundamental point of the book. it also teaches that philosophical reﬂection is itself our means of escape. given these seemingly more modest aspirations.
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. their capacity to mystify and captivate.The liberating word Still. liberation comes only by way of the most uncertain of paths.” early and late. And that is to say that his attempt to free us from metaphysical confusion can just as easily serve to lead us more resoundingly into its depths.

.

An even more extended discussion of the issue is found in the “Big Typescript. and the use of the term erloesende and its cognates at PG 193. 1998. Ricketts (1996). and will be discussed in some detail in this Introduction. 75. The clash between these new readings of the Tractatus and the more traditional interpretations. 99. 2000). Ramsey (1931). I am here alluding to – and placing this book among – the cluster of “nonstandard” interpretations of the Tractatus that would include Cerbone (2000). Conant (1989. but will occasionally take recourse to the Pears/McGuinness translation. Witherspoon (2000). 1991. Black (1964) Stenius (1960). but without completely embracing what she calls a “metaphysical” position.” sections 86–93 (PO 161–199).NOTES
Preface 1. 6. 101. Goldfarb (unpublished). 1993. 87. See PI 97–133. Dreben (unpublished). 1991b). Introduction 1.
3. in the context of a much broader and more detailed survey of Tractarian interpretations. This translation is from the original Ogden version of the Tractatus. 137
2. forms the immediate backdrop of this study.
4. Kremer (1997). CV 33. Friedlander (1992) might be included here as well. Diamond (1991a. Winch (1992). and D 69. McGinn (1999) discusses this conﬂict and attempts to develop a kind of synthesis of the two approaches. most recently defended by Hacker (2000) and Pears (unpublished). See also the occurrences of the phrase erloesende Wort at NB 39 and 54. in press). Biletzki (in press) also offers an overview of the debate. 5. I will generally rely on the Ogden version for quotations.
. Floyd (1998. Reid (1998) offers a criticism of the Conant/Diamond position in particular.

54. 8. it must explain the remarks in the Notebooks on pages 45 and 50. and not simply as an expositor of Wittgenstein. 15.
13. 2000) and a number of other commentators have further elaborated the Diamond view. 16. 185). Hacker espouses such a position in his classic work Insight and Illusion (1986). also. Hacker (1986). He presents a more forceful argument for this view. Such attempts to disregard or downplay the signiﬁcance of 6. Pears (1987). p. the real force of characterizing logical proposition as tautologies is itself. it remains for such an interpretation to account for 4. very delicate and open to a variety of interpretations. As I mention in footnote 2. Warren Goldfarb (unpublished) independently argued for a related position in an unpublished but frequently noted 1979 paper. in his recent response (2000) to Cora Diamond’s way of reading the Tractatus. See Dreben and Floyd (1991) for an excellent discussion of the shifting senses of the notion of tautology. like almost everything in the Tractatus. Anscombe (1959). 19. And that is to say that there is no easy or straightforward way to settle this interpretive dispute. 138
11.
17. James Conant (1989. Hintikka and Hintikka (1986). 1991. Dreben (unpublished).
18. 14. their signiﬁcance too can be downplayed. Diamond (1991. 37–8 of Philosophy and Logical Syntax). He in fact explicitly acknowledges that his own position may differ from that of the Tractatus (see pp. Carnap (1979) for a statement of this way of responding to Wittgenstein’s text. We must of course bear in mind that Carnap is writing always as a philosopher himself.
.Notes to pp. Instead. and Floyd (1998. Hintikka and Hintikka (1986). 1993. in press) have also more or less independently articulated a similar interpretation of the text. suggest (as Pears did in a 1998 meeting of the Boston Colloquium for Philosophy of Science) that this remark was inserted by Wittgenstein at the close of the book simply as a means of protecting himself from criticism. Diamond (1991). But my central point is that the invocation of such passages is unlikely to be conclusive. Still. some justiﬁcation for this strategy can be offered: one might. 10.54 need not be understood as mere oversights on the part of commentators. Geach (1976). where Wittgenstein is already found to be asserting that claims about the existence of simple objects – the sort of seemingly meaningful claim that dominates the opening section of the Tractatus – are nonsensical. See. for example. Ramsey (1931).
12. 3–6
7. Of course. 9. however. 1998. In the language of the Tractatus. whose implication would seem to be much the same as 6. we could say that Carnap views such formal assertions as sinnlos rather than unsinnig.1272 at the center of the Tractatus. for example.

” the sort of sentence that Wittgenstein explicitly dismisses as a “nonsense pseudo-sentence” (TLP 4. Diamond (1991. Aside from my concerns. “ ‘nonsense’ cannot really be a general term of criticism” (p. philosophical nonsense resists logical segmentation and thus cannot be understood as resulting from the illegitimate combination of intrinsically intelligible components. 157–8). pp. 6–12
20. in her response to Goldfarb (1997. 216. for Wittgenstein. 31. p. Instead. 1993. it seems that we should say that the distinction. understanding it as the question of whether Wittgenstein has “a general approach to the issue of irresoluteness. p. Conant (1991. 27. Diamond (1991. pp. Conant (1991. p. between what Conant calls the “substantial” and “austere” conceptions of nonsense (2000. and so forth. arguing that. want to say something like this: ‘Wittgenstein’s (or Kierkegaard’s) teaching cannot be stated. See Diamond (2000). p. 244–50. p. p.Notes to pp. implicit especially in 5. Indeed. Diamond. Conant (1989.” 25. 26. the conception of logic as tautologous. pp. and as such should be seen as having the same status as the show/say distinction. 21. pp. 198) also emphasizes this distinction. for Wittgenstein. p. Diamond (2000. Goldfarb (1997) again makes something like this point with his remark that.” She does not. But clearly her contention is that his own seemingly positive assertions have exactly the same status.1272). about leaning too heavily on this particular formulation. 33. 344. pp. 29. 28. pp. 23. 80). p. 158–60). 130) makes a similar point. p. Goldfarb (1997. 194–5) tends to emphasize this point quite strongly as well. 197) introduces this expression as a way of describing “a is an object. p. pp. over and over again. suggesting that Diamond surreptitiously introduces a distinction between “plain nonsense” and “transitional nonsense. 96) as an example of the kind of thing Wittgenstein has in mind whenever he speaks of philosophical nonsense. 24. 32. 176) belongs to the internal apparatus of the Tractatus. “Jabberwocky” is put forth by Diamond (1991. attempt to provide a determinate answer. however. 2000. Diamond (2000. Reid (1998. Hacker (2000. appears to acknowledge the problem. 71). 95–114). Hacker (2000. 361) makes a similar point (although in a rather more contentious manner). 341–2. 1998. 362) tries to use something very much like this claim as a reductio of the Conant/Diamond reading of the Tractatus. p. p. 266) presumably is saying something of this sort when he holds “I.” 139
. 2000. 30. 22. 70–2) argues in much the same way in his discussion of Diamond’s The Realistic Spirit. it can only be shown’. discussed above. 44) makes a similar assertion. Floyd (in press.4733. I also worry that it can lead to attributing to Wittgenstein just the sort of theoretical doctrine that Conant most wants to avoid – as if Wittgenstein’s central aim were now understood as one of giving an elaborate account of the nature of nonsense.

In viewing this most dogmatic-seeming of texts as intrinsically dialectical. I once meant to include in the preface a sentence which is not in fact there now but which I will write out for you here.e. for example. because it will perhaps be a key to the work for you. 12–13. then. rather. 36. that there is at least a family resemblance amongst all these various uses of the notion.. Note here how a speciﬁc alteration in one of the claims of the Tractatus. The key passage from this letter reads: “The book’s point is an ethical one. would not appear to consist in a false assertion in the ordinary sense but. I am to some extent following Dreben (unpublished). 41. 37. was this: My work consists of two parts: the one presented here plus all I have not written. Hacker (2000. if I may be forgiven the employment of a piece of Wittgenstein jargon. After remarking that he quite rightly held in the Tractatus that those forms could not be speciﬁed in advance. pp. Conant (1991. The answers to philosophical questions must never be surprising. however. just in the implied assimilation of philosophical claims to those claims that could be false (or true). 40.Notes to pp. such an assimilation. p. Wittgenstein suggests. 371–82) emphasizes this point as part of his argument against the Conant/Diamond reading of the Tractatus. At the time I wrote in a manuscript of my book (this is not printed in the Tractatus). 35. 3). My book draws limits to the sphere of the ethical from the inside as it were. and the seemingly theoretical description of the earlier position as a “mistake. it is not clear that they all understand “dialectical” in just the same way either). the idea of dialectic is rather slippery – I do not attempt to deﬁne this term – and I make no claim to be using it in exactly the same sense as any of these authors (indeed. What I meant to write. pp. runs counter to the spirit of the Tractatus. 12–19
34. And it is precisely this second part that is the important one.
140
. we should have to be able to think what cannot be thought)” (TLP. had not clearly understood this and offended against it” (VC 183). Only in recent years have I broken away from that mistake. Wittgenstein’s 1931 discussion of the Tractarian understanding of the forms of the elementary propositions. Needless to say. Floyd (1998). I myself. 39.” go along with Wittgenstein’s suggestion that he had not truly understood the anti-theoretical character of his own thinking. we should have to ﬁnd both sides of the limit thinkable (i. Again this point is essentially made in the Preface. 352–4) makes a similar point. and I am convinced that this is the ONLY rigorous way of drawing those limits” (LF 95). I think it is safe to say. 1997). Putnam (1998). in other words. 38. In philosophy you cannot discover anything. and Goldfarb (unpublished. See. See pp. however. The mistake here. See CV 32–3. he goes on: “Yet I did think that the elementary propositions could be speciﬁed at a later date. when Wittgenstein asserts: “In order to be able to draw a limit to thought.

This will be discussed in Chapter II of this study. p. but also fundamentally obscures Wittgenstein’s real purpose. universals. In light of this point. Thus. pp. also 2. 27–8. See Mounce (1981. part of his purpose in introducing the notion in the way that he does is precisely to lead us away from this kind of logical categorizing. for example. Moreover.g. is in fact explicit about the dual role of the term “logic”: “Logic may mean two things: (1) a logical calculus as e. 14–17). Wittgenstein. particulars. p. 5. 4. 325– 41). 2. 22–8
Chapter I 1. Friedlander (1992. pp. yellow. A tone must have a pitch. the Principia Mathematica (2) the philosophy of logic” (CL 110). the standard attempt to accommodate Tractarian objects within traditional philosophical categories seems particularly misguided. 3. p. Cf. 26). 8.0131: “A spatial object must lie in inﬁnite space. in a discussion with Desmond Lee in 1930 or 1931.64 alone seems to suggest the hollowness of this whole debate. 19). Instead. and so forth. Pears (1987. pp.” Once more. 66– 72). To attempt to explain the real nature of objects is to be engaged in an endeavor that is not only fruitless. it has often been by attempting to place the text into some other standard philosophical niche. but it must have a color. See. etc. pp. A good deal of the literature on the Tractatus in fact involves debates over which one of these sorts of notions Wittgenstein “really” means when he speaks of an object.. 6. Dummet (1991). 5. green. Williams (1974) argues that the Tractatus is in fact a (transcendental) idealist tract. A speck in a visual ﬁeld need not be red. as it turns out.g.Notes to pp. e. or what have you. 75–85). 7. 10. for example. 85–107). even when such a view has been challenged. For it is not simply that Wittgenstein suggests that. and Fogelin (1996. a color space round it. pp. 83) also characterizes the role of the object in the Tractatus in something like this manner. we cannot settle a priori whether objects are sense data. Nonetheless. referring to the object as a “condition for the possibility” of the fact. Weinberg (1966. 11. See “Function and Concept” (CP 141). (A point in space is an argument place). it has. many commentators have insisted on characterizing the Tractatus as an essentially realist work. the Tractatus is clearly anticipating 3. Hacker (1981. see. Allaire (1966. this tone taken together with all the other pitches it could assume. the object of the sense of touch a hardness.. while Copi (1966) and Anscombe (1959) see Wittgenstein as advocating a certain brand of nominalism. etc. so to speak. Wittgenstein makes it clear that the object is to be identiﬁed with the thing in its space of possibilities: it is this red speck taken together with its capacity to be blue. At this point. Pears (1987. 9. Stenius (1960).221: “Objects I can only
141
.

72). See.
20. Signs represent them. A possible sign must also be able to signify.
17. 23. – The proposition that depicts it functions as a description. see pp. 28–36
name.
. pp. Friedlander (1992) makes a similar point. a term that Ogden here renders as “represent. pp. The leading question might be expressed as: Given that this is what the world must be. Black (1964.
16. I translate as “represent. See. This is the position taken by Black (1964. 84–5. pp. for example. Schwyzer (1966. NB 52: “The name of a complex functions in the proposition like the name of an object that I only know by description. p.Notes to pp. again like Friedlander.” But we have seen that a quite different conception of simplicity would seem to be operating in the Tractatus. it is sufﬁcient to bear in mind that a single Sachlage appears to comprise both an existent and a nonexistent Sachverhalt. 23–5). 427. Wittgenstein now turns to consider what is necessarily involved in any symbolic representation of the world.
15. 277–8). For the time being. 58–62). 19. for example.
13. Stripling (1978. pp.” Cf. provided ‘language’ is taken to include any system of signs. TLP 5.473. not what it is. The signiﬁcance of this third way of speaking a fact will not be discussed until Chapter III. that is adequate for making all possible assertions about reality” (1964.
21. for example. I suggest that thus framing the issue in terms of a need for “immediate contact” between language and the world stems from viewing Wittgenstein as ultimately resting on a Russellian notion of “knowledge by acquaintance.” Cf. in order to be capable of representing the world adequately? The task may be called. 77–8). 22. not necessarily verbal.” always as “present. p. what must language be. Here I follow Friedlander (1992) in translating vorstellen. See.” This is done to mark a systematic distinction from Wittgenstein’s use of the term darstellen. 75–81).” Recall from the Introduction (pp. 19–21). Black’s introduction to the Tractatus’ discussion of the picture: “Having concluded this account of the world as a mosaic of atomic facts embedded in logical space. Mounce (1981. I cannot assert them. which. Note that also mentioned here in connection with the negative fact is the term Sachlage (translated by Ogden as “state of affairs”). that of clarifying the essence of all language. also this remark from two days earlier: “ ‘Complex sign’ and ‘proposition’ are equivalent” (NB 52). in Wittgenstein’s own phraseology. Cf. pp. Principles of Mathematics. I can only speak of them.” The role of darstellen will be discussed in Chapter III. pp. 14. 96) also focus on this aspect of the picture theory. 32.
18. p. as well as by Mounce (1981. 14–15) our contention that the whole Tractatus can be conceived as an attempt to characterize precisely the philosophical question. which directly mirrors language from the opening remark of the Notebooks: “Logic must take care of itself. and Friedlander (1992. A proposition can only say how a thing is. 142
12.

the clicks of a ﬁnger with the “2” and the “4” of each measure. Cf. NB 108. If we dwell upon it and do not try to get beyond it. no. about how their forms only emerge through the structure of the atomic fact. The Tractatus is in this way sometimes assumed to rest on the postulation of a fundamental “isomorphism” between language and the world. The same point could be made using the idea of music. But that we can represent the time in some such way is not arbitrary – it is integral to this piece of music being the kind of thing that it is (as is evident if we think of the ludicrousness of the attempt to clap along with a novel). because the external form of the clothes is constructed with quite another object than to let the form of the body be recognized. TLP 4.” Cf. For. This point will be key in understanding how Wittgenstein views the sense of a proposition.Notes to pp. pp. Black (1964. say. so that from the external form of the clothes one cannot infer the form of the thought they clothe. 143
. 61) and Stenius (1960. as we shall see. 38–41
24. it is a central tenet of the Tractatus that the proposition’s sense – the thought that it expresses – is not given by any external features of the propositional sign. 28. 69. clap along with a song is in one sense arbitrary: there is no necessity that we correlate hand claps rather than. the metaphor that we ﬁnd at 4. among others. 31. Cf. Recall that I always use this word as a translation of Wittgenstein’s vorstellen. 32. This difﬁculty in assessing Wittgenstein’s real orientation toward the question at hand calls to mind his remark in Zettel 314: “Here we come up against a remarkable and characteristic phenomenon in philosophical investigation: the difﬁculty – I might say – is not that of ﬁnding the solution but rather that of recognizing as the solution something that looks as if it were only a preliminary to it.002: “Language disguises the thought. the mathematical notion of an isomorphism conceives of a 1– 1 function mapping one independently given domain onto another. 26. pp. Hacker (1986. if we give it the right place in our considerations. Wittgenstein would then say that the possibility of representing the rhythm of this song by means of hand claps ultimately depends on a commonality of form. The difﬁculty here is: to stop. whereas the solution of the difﬁculty is a description.011–4. I believe. – Not anything that follows from this. this itself is the solution!’ This is connected. also this remark from “Notes on Logic”: “Distrust of grammar is the ﬁrst requisite for philosophizing” (NL 106). 25. By contrast. 29.0141. Here one begins to feel the real force of the earlier point about the “simplicity” of objects.” 27. He also seems to suggest this idea in NB 37. p. The fact that we can. for example. 91–6). put forward this idea. 90–1) prefers the term “homomorphism” but holds to the same basic notion of the centrality of this “hypothesis” to the Tractatus’ view. with our wrongly expecting an explanation. 30. ‘We have already said everything.

then. this notion is thus quite connected with the account of the so-called logical constants. from darstellen as well). 37. even 144
. as one of the fundamental categories of thought or language that will be made manifest in the elementary propositions. such a hierarchy of languages. 41–7
33.Notes to pp.181 (“If the pictorial form is the logical form. Pears (1987.”): it does not seem to make sense to speak. According to Friedlander. We may leave it an open question as to whether the Tractatus will ultimately count space as one of the logical forms – that is. The distinction. Russell (p. The issue of the relation between the notions of pictorial and logical form and their relation to Wittgenstein’s conception of analysis will be addressed in the next chapter. then. is between a picture’s relation to some speciﬁc set of facts and its fundamental role as a picture: just by virtue of being what it is. 35. See pp. a picture (Bild) depicts (abbildet) reality. For. the logical form has to do with how we use the picture as a whole to state something about the world. as the condition of the picture-fact’s capacity to represent some particular state of affairs. Now. nothing would seem to preclude the possibility of another language serving this function. 136) also raises this issue. he holds. I take as extremely important this distinction between the inner composition of the picture and its use in representing particular states of affairs. p. 143). 39. p. 38. might indeed be inﬁnite. 12–13. It is thus not yet decided whether “space” is put forward as an example of the results of logical analysis or as a mere analogy. See also Introduction to the current study for a more general discussion of this issue. Here one is of course reminded of Russell’s response to the show/say distinction in the Introduction to the Tractatus. this assimilation would appear to ﬂy in the face of 2. especially of Cora Diamond’s way of criticizing the standard reading. then the picture is called a logical picture. 40. 144). Friedlander suggests a distinction between the pictorial form. 2. as the condition of the possibility of the picture as a fact. while it may be impossible to express the underlying structure of a language in that same language. 34. it only “depicts” reality or the world. p. as will become increasingly evident. But I do not believe that the notion of logical form is to be connected with the latter. 143). Chapter II 1. Pears (1987. p. as we shall see. Note that the term abbilden is thus distinguished from vorstellen (and. and the logical form. 36. 102–07 of Friedlander (1992) for his discussion of this issue. Pears (1987. Whereas a picture “presents” the existence and nonexistence of a certain set of atomic facts (and “represents” a possibility of such facts). 23) famously suggests that. if nothing else. Pears (1987. See pp.

pp. 88– 91). pp. 98–101).g.
9. acquaintance with a logical form is a prerequisite for the possibility of judgment is discussed by Russell in Theory of Knowledge (see.
7. e. pp.1432. 51–2. the “relation” between picture elements and their real world counterparts is not a genuine one. 111). also Fogelin (1976. Unlike Black. for example. 99. pp. for all of whom this remark provides evidence that properties and relations are not Tractarian objects. it misses what we have suggested to be Wittgenstein’s real point about our relation to those forms – how it is nonsense to suppose that they could be given a priori. From what we have already seen about Wittgenstein’s conception of objects. in general. one might say that Frege’s resorting to metaphor here is an indication that. as well as in The Philosophy of Logical Atomism. a spatial picture. who distinguishes the “homologous” relation holding between the arrangement of picture elements and reality in a logical picture from the “identity” that characterizes the corresponding relation in.
5. none of these issues is directly relevant to the real concern of 3. Ricketts (1996). But in its insistence on relying on understanding the basic constituents of the atomic fact in terms of traditional philosophical categories. of course. 47–51
hypothetically. 249–51). 83–4).. it is a contingent or nonessential feature of the particular pictorial method of representation used in our example that in it no proxies for spatial relations will appear. The notion that. 38. pp. like Wittgenstein. pp. Principles of Mathematics. Anscombe (1959. Or. pp. e. but the problem of the unity of the judgment has a similar structure. In this respect. such an interpretation cannot.
8. Sellars (1966. Cf. pp. e. Copi (1966. Evans (1966. I am reading Wittgenstein as ultimately concerned to show that. See. we could say. Here I am to some extent echoing the position of Black (1964. as I argue immediately below.
4. pp. 133–5). whether we speak of a logical picture or a spatial one.. 39–43) for a good account of Wittgenstein’s later rejection of the picture theory. Wittgenstein’s discussion is in fact linked to Russell’s early worries over accounting for the peculiar unity that seems to distinguish a proposition from a mere list of its constituents (see. however. of how the notion of a picture shifts from a way of characterizing (in some sense) the proposition to a way of describing the basis of the drive toward philosophical theorizing. 177–8). be altogether incorrect.
10. of a situation in which the pictorial form is the logical form if these notions correspond to the very different dimensions of the picture that Friedlander describes. This was Ramsey’s (1931) view of the Tractatus’ position. By this time. and. See Stern (1995.
6.” Now.Notes to pp.g. in addition to acquaintance with objects. Moreover. Frege uses this language in “Function and Concept” and “Concept and Object.g. more recently. he recognizes the impossibility 145
3.
. Russell no longer countenances propositions as genuine entities and thus is not concerned to account for their unity. 19–20) on this issue..

Note that in “Some Remarks on Logical Form.” Here this key passage from Philosophical Grammar is especially pertinent: “Formerly. See pp.
16. he imagines setting up a coordinate system that would enable us to represent the shape and position of every patch of color in our visual system. 15. See. It is essential then to see how contrary such a position is to the Wittgensteinian view.03: “In the atomic fact objects hang one in another. 14.. just as they are.). but this has not always been the case. 12. would be part of the force of Ricketts’ insistence on the primacy of the judgment in Frege’s thought (see. I spoke as if there was a calculus in which such a dissection would be possible.” it is just this sort of procedure that Wittgenstein describes when he offers an example of the partial analysis of the sentence “Color patch P is red.
17. This. etc. Even so. for example. I take it. logically completely in order. as I am presenting it. by setting up a mode of representation that allows for the full range of possible color ascriptions. How then.563: “All propositions of our colloquial language are actually. 74–80). like the links of a chain.521 apparently rebukes Frege and Russell for confusing generality with logical sum/product. and I used to believe that philosophy had to give a deﬁnitive dissection of propositions so as to set out clearly all their connections and remove all possibilities of misunderstanding. just as Wittgenstein in Philosophical Grammar claims that it did (see PG 268 ff. I vaguely had in mind something like the deﬁnition that Russell had given for the deﬁnite article. In this conception of analysis. and thus exhibit once for all the connections between the concepts and lay bare the source of all misunderstandings. I myself spoke of a ‘complete analysis’. we are called back not only to 2.
13.g. 41 ff. e. to deﬁne the concept say of a sphere. Frege does seem to speak as if there might ultimately be a fact of the matter with regard to the question of the nature of the relation of function and object.15.
. Hintikka and Hintikka’s (1986) attempt to construe such propositions as statements about “immediate experience” (pp. he makes clear that it would be treated in the same manner – that is. 51–6
of giving any sort of genuine account of the proposition’s unity. only such a fact is unavailable to us. of course.” Thus.” (PG 211).Notes to pp. This later criticism has long puzzled commentators. Ricketts [1986]). can Wittgenstein have been involved in the same confusion himself? The 146
11.” One might suppose that this remark would have served to steer commentators away from vain speculation about possible examples of Tractarian elementary propositions. And here. While he offers no sample analysis of “red” itself. Tractarian readers have wondered. See also TLP 5. I suggest we can see how the Tractatus might be said to assimilate generality to logical sum or product. certainly such a perception is given by Frege’s remark that the distinction between functions and objects is “founded on the nature of our language” (CP 194). and I used to think that in a similar way one would be able to use visual impressions etc. but also to 2. since the Tractatus at 5.

is that while the early Wittgenstein attempts to distinguish the grammar of generality from that of the truth functions. many commentators. for Symbolism in which a sentence ‘means’ something quite deﬁnite. however. that if I have two thoughts I must know whether they are the same.62 that what solipsism means is quite correct – is already evident in these passages. then. The attraction of solipsism for Wittgenstein – part of the reason why he will say at 5. beginning with Russell in the Introduction.
19. in supposing that the sense of a quantiﬁed statement could be captured through a speciﬁcation of its instances. 68 of The Foundations of Arithmetic. See also Pears (1987. 112) makes a similar point. that if I have one thought I must know what thought it is. See. so that what we assert is never quite precise” (p. language is always more or less vague.Notes to pp. transparent to us. My suggestion. for in requiring that concepts be deﬁned for all arguments he too is acknowledging that the meaningful assertion in some sense cannot leave any possibilities open. that is to say.
. i. 24. we must come to see here the insubstantiality of the claim that logical analysis deals only with “my” sense. He does not accept. Cf. for example. 23. Thus Russell writes: “[Wittgenstein] is concerned with the conditions for accurate Symbolism. have in fact assumed Wittgenstein’s talk of “determinateness” to suggest that he is working within something like a Fregean framework. among other places.
20. p. 73. 40). Hylton’s (1997) claim: “Such a conception of sense is possible because Wittgenstein does not accept that our thoughts are. he comes to see later that he had not done this with sufﬁcient sharpness. Ironically. p. Just as he will then deﬂate the “truth” of solipsism by equating it with pure realism (see TLP 5. Wittgenstein is implicitly committed to viewing the quantiﬁer as somehow derived from disjunction or conjunction.
21. 8). 57–8
above discussion brings out how. 92). p. we might say that something like the same insight lies behind Frege’s way of demanding determinateness of sense. n. Nonetheless. But Frege unwittingly undermines his own insight (at least from Wittgenstein’s point of view) by supposing that such determinacy must be somehow secured by us prior to the application of my concepts to the world.φx would be found” (PG 268).
22.64).e. The way in which such a claim might be said to be misleading should become apparent as we go along.. so to speak. where Frege asserts that a proper deﬁnition of number must be able to tell us whether or not Julius Caesar is a number. and so on” (p. This in fact is precisely how he describes his mistake in Philosophical Grammar: “The [explanation of (∃φx as a logical sum and of (x).φx as a logical product] went with an incorrect notion of logical analysis in that I thought that some day the logical product for a particular (x). Black (1964. This is stated more or less explicitly by Frege in “Function and Concept” (CP 148) and “On Sense and Reference” (CP 169). This presupposes that circumstances might arise that would lead us to shift our assessment about the meaningfulness of our assertions: for 147
18. In practice.

for example. it turns out. this remark from the ﬁrst appendix to “Notes on Logic”: “It is to be remembered that names are not things. as Dreben (unpublished) has pointed out. 146). Moreover.Notes to pp. but classes: “A” is the same letter as “A. this is nothing but an admission of the intrinsic indeterminacy of sense and hence a fundamental misconstrual of the role of logic.325 suggest.
. this 148
25.” This has the most important consequences for every symbolic language” (NB 102). suggesting that “Wittgenstein’s own programme for ‘logical syntax’ can properly be viewed as an attempt to accomplish what Russell was reaching for in his theory of types” (p. 55–6. a speciﬁcation of a formal language in terms of a set of formation rules and a set of transformation rules. See pp. 27. but that is not to say that this language “rules out” expressions formed from such notions (and. that aim is to rule out what Wittgenstein terms “nonsense. besides.
30.324 and 3. Black (1964). See especially pp. 35. fails to be deﬁned for some argument “a” (an argument that I may not have anticipated when introducing the concept). a little reﬂection will reveal that a syntactical approach in Hilbert’s sense couldn’t satisfy the aim of Tractarian logical syntax. if the avoidance of nonsense were simply a matter of refraining from the use of certain terms. See VC 46.
34. preclude expressions like “The world is everything that is the case” or “2 2 is at 3 o’clock equal to 4”? It is true that the mathematical logician will typically have no reason to include a name for “the world” or a predicate denoting “is at 3 o’clock” in his language. Frege in this way imagines a kind of divorce between language and its users – as if we could draw a general distinction between what I think I mean by my utterance and what I in fact mean. I will conclude that this judgment. 31. Principles xv. familiar from Russell’s famous distinction between knowledge by acquaintance and knowledge by description. This conception of the name is. See Ricketts (1986. as 3. assuming that. if my judgment contains a concept “φ” which.” For how would such a standard meta-mathematical approach. though. But this seems to imply that it is up to the world ultimately to determine whether or not my judgment makes sense. pp.
32. 33. For Wittgenstein. 142–4. 59–65
Frege. 29. This is a conclusion reminiscent of Pears’s (1987) reading of the picture theory. of course. appears to understand Wittgenstein’s criticisms in this manner. 65–96). Here I suggest that we can see the origin of Wittgenstein’s interest in the “seeing-as” phenomenon discussed especially in Part II of Philosophical Investigations.
26. Cf. It is indeed just this interpretation that Carnap builds on in his The Logical Syntax of Language. and all those containing “φ” lack a Bedeutung. 28.

The point. Russell. The proposition corresponds to the fundamental co-ordinates. This recognition leads to the so-called color exclusion problem that is discussed in “Some Remarks on Logical Form.
40. though. Frege in “Concept and Object” 149
36.g. Black’s technical interpretation of the criticism.” e. The point here is not that the grammatical investigations characteristic of his later thought involve instituting a priori restrictions on sense of the kind that we ﬁnd in the theory of types. See Introduction to the present study. since Wittgenstein comes to see that color cannot ultimately constitute one of the logical forms. After all. p. of course. is that Wittgenstein’s approach is more ﬁnegrained and will thus acknowledge at least those distinctions drawn by the theory of types. 43. 65–9
could be accomplished in ordinary language as easily as in a formal language). Hintikka and Hintikka (1986) and their claim about Wittgenstein’s commitment to the “ineffability of semantics. See Grasshof (1997) for a discussion of the inﬂuence of Hertz. for example. “grammar” is really seeking the same end sought by Russell – the avoidance of a certain sort of nonsense. This example is used only for the sake of illustration.331–3. 145). as is evident from his characterization of these passages as “a digression.
42.
. we no doubt see the inﬂuence of Wittgenstein’s training as an engineer. more speciﬁcally. Instead. as is illustrated in this example.. whereas. not to suggest that Tractarian differences of Bedeutung will correspond precisely to Russellian type theoretic distinctions. the importance for him of Hertz. Admittedly.
41. the method of symbolizing – is the system of coordinates which projects the situation into the proposition.
44. who holds that. can only meaningfully be substituted in the ﬁrst).” See. p. by contrast. This would seem to be the position of Cora Diamond. would regard “x is brown” and “x is heavy” as belonging to the same type of propositional function. for Wittgenstein.
37. 38. for example. “the whole philosophical vocabulary reﬂected confusion” and hence that “we are all Benno Kerry’s through and through” (1991. Wittgenstein would distinguish them (since “the surface of the table. but also. 184). NB 20: “The internal relation between the proposition and its reference. It is presumably this sort of idea that leads Wittgenstein in Philosophical Remarks to declare that grammar – the descendant of Tractarian logical syntax – “is a ‘theory of logical types’ ” (PR 7). can only be maintained by ignoring the context of 3. although one that draws a very different picture of the nature of the Tractatus.” In the persistent metaphor of the coordinate system.” albeit “a highly interesting one” (1964. Wittgenstein is saying that by describing clearly the role of certain problematic expressions.Notes to pp. as we have seen.” This is. it is not entirely clear that such objections are in the end effectual against Frege either. Cf.333.
39.

For even in “Concept and Object” he speaks of his use of the term “concept” as “purely logical” (CP 182). Such formulations. whatever the speciﬁc manner of expression chosen.
47.
48.g. that is. But early on in his 150
45. in every analysis that is to count as complete the possibilities of combination of the simple signs – the sign system’s “mathematical multiplicity” – will be the same. The notion of mathematical multiplicity also can help us make clearer Wittgenstein’s claim about the uniqueness of analysis. in such a way that its resolution would be different in every propositional structure. since it represents an example of a language in which certain kinds of signs are always used in this way. to refer to something that is intrinsically predicative in nature.Notes to pp. The Begriffsschrift could then in fact be seen as helpful in clarifying what that means..3442: “The sign of the complex is not arbitrarily resolved in the analysis. he seems to suppose that the actual carrying out of an analysis into elementary propositions is no part of the task of logic (presumably just because it has an apparent a posteriori character) and that its completion would therefore be of no logico-philosophical interest (see. such a choice is obviously arbitrary. a claim that is in fact reiterated at 3. On the other hand. Such an interpretation of Frege’s thought brings him closer to Wittgenstein. Frege does invite questions about the status of his Begriffsschrift. since the focus here is only on characterizing a particular expression. describe Wittgenstein’s later recognition of the color exclusion problem in just these terms: as a result of reﬂection on what makes sense to say in ascriptions of color. though. while perhaps helping to make clear why Wittgenstein suggests that the attempt to give an a priori speciﬁcation of logical form is incoherent. of logic generally – just the kind of question that I claim the Tractatus is most concerned to get us to ask. suggesting that it is meant to reﬂect the necessary structure of our language. but quite central question to answer if we are to understand the development of Wittgenstein’s thought.
46. Again we are called back to the opening of the Preface and the prerequisite for understanding the book’s point that we have the same or similar thoughts as its author. Wittgenstein comes to see that his so-called ab-functions – the truth tables – do not have the right multiplicity (at least for the task he envisioned for them) and therefore must be either modiﬁed or rejected. 69–70
acknowledges that he is using the term “concept” in a special sense. Frege does seem to want to claim more than just the right to employ a term in his own peculiar sense. In brief. Indeed.” To hold that there is a unique analysis of the proposition “The watch is on the table” is not to say that all acceptable analyses will literally make use of coordinate systems. as Cora Diamond would have it.5571). We might.
. In this case. I would suggest that. appear to leave open the possibility of an a posteriori completion of the task. in the Tractatus. Instead. e. is this not what the Tractatus’ own program of analysis amounts to? This is a difﬁcult. 5. in fact. the claim amounts to the assertion that.

that it is the task of logical analysis to discover the elementary propositions. that the notion of what we can think serves as a criterion of what is logically possible. 70–5
“middle period” he comes to regard his Tractarian reliance on the possibility of such an enterprise as illicit. This point will be very important both in the Tractatus’ account of tautology and in its characterization of the general form of the proposition. along with “property” and “relation” to have shifted its ordinary usage. We are unable to specify the form of elementary propositions. Thus. but rather that he comes to see that the supposed sharp distinction between the a priori and the a posteriori must itself be given up. It now should be evident that “object” in this context would be said by him to designate a form. Thus I used to believe. Only in recent years have I broken from that mistake” (VC 182). Cf. It was clear to me that here at any rate there are no hypotheses and that regarding these questions we cannot proceed by assuming from the very beginning. but rather that these two notions are themselves internally related.
. and thus. and that is the conception that there are questions the answers to which will be found at a later date. as he makes clear in this remark to Waismann: “There is another mistake. the grammatical inquiries that we ﬁnd in the Investigations are really attempts to carry out (albeit in a revised form) the purely descriptive enterprise envisaged for Tractarian logical syntax. That is. etc. some commentators refuse to believe that he really intends to dismiss as incoherent the ideas at the center of the philosophy of logic.
52.123: “Here to the shifting use of the words ‘property’ and ‘relation’ there corresponds the shifting use of the word ‘object’. It is held that. although a result is not known. I suggest that “breaking from that mistake” comes to involve actually engaging in the analysis that is only spoken of from afar in the Tractatus. Despite Wittgenstein’s forcefulness in this remark. This is not to suggest that philosophy becomes for the later Wittgenstein an a posteriori discipline. 53. he then had remarked how it is “unthinkable that these two objects should not stand in this relation” (TLP 4.557: “The application of logic decides what elementary propositions there are. there is a way of ﬁnding it. a possibility of a color. What lies in its application logic cannot anticipate.” With this understanding of the ambiguity inherent in the notion of an object we also can make sense of the parenthetical remark at 4. and that was quite correct too. which is much more dangerous and also pervades my whole book. Black (1964) insists that the term “pseudo-concept. for example. 90–4.
51. We shall discuss this point in greater detail on pp. Yet I did think that the elementary propositions could be speciﬁed at a later date.” It is not. Implied here is the complete coextensiveness of “thinkability” and “logical possibility.” Wittgenstein above had been commenting on the “internal relation” of brighter and darker that obtains between two different shades of blue.23). for example. 50.Notes to pp.” which Wittgenstein uses in 151
49. as Carnap does. in other words. also 5. that the elementary propositions consist of two-place relations. I wrote.

Stenius (1960.Notes to pp. 37 ff. most concerned to undermine – it is at odds. and hence that the Tractatus’ attempt to perform a kind of wholesale eradication of philosophical nonsense was illegitimate. “should not be read pejoratively” (p. “pseudo-concept” constitutes. See pp. The heart of the later Wittgensteinian rejection of the Tractatus is. We are here called back to the Introduction to this study and the discussion of the difﬁculties inherent in the endeavor to characterize the central point of the Tractatus. give it a new use. we can use this new distinction between proper and pseudo-concepts to go on and do legitimate philosophical work.” “fact. then. Thus the later fascination with following a rule and how one step cannot be regarded as determining the next: this is just a way of tearing away the remaining shreds of any sense of an underlying a priori structure. For his later insistence on staying at the level of the particular case reﬂects precisely the insight that one can always (or almost always) make sense out of a form of words. in the manner of Carnap (whom he quotes in this context). he appears to assume that these words function more or less as synonyms in the Tractatus. 98–9) notes the distinction.” darstellen as “present”).. 14–15.” Now. 76–81
connection with “object. pp.” etc. 54. even if his interpretation of these notions is ultimately somewhat different from my own. 2. however. for him. Again I attribute this way of drawing the distinction between the Tractarian terms vorstellen and darstellen to Friedlander (1992. in effect. the crucial distinc152
. 55. 3. I am following him in rendering the former always as “present” and the latter “represent. we might say. Indeed. 103–07). For he comes to see the notion that all the Tractarian apparatus is somehow “given” along with a certain view of logic as a remnant of the “a priori-ism” that he is. Nonetheless. not only with his later beliefs. throughout his life. would be anathema to Wittgenstein. 202). just the recognition of such structure as illicit. This. it is not at once clear just why it wouldn’t be pejorative to call a concept “improper. as it only serves to mark a contrast with “proper concept. no more than a technical term.” But presumably Black supposes that.
Chapter III 1. pp. See pp. but also with the very perspective that the early text was seeking to present. I would suggest that the full recognition of how one’s fundamental point can be shifted in this way – how one’s attacks on the philosophical tradition can be neatly turned to form a new move within that tradition – motivates in large part the style of Wittgenstein’s later writing. translating Wittgenstein’s German by different English terms (vorstellen is rendered by him as “depict.” Few commentators have focused on Wittgenstein’s use of these terms.

as it were. as 5.
13. Note that Wittgenstein does use the same term here as in the Tractatus to describe this aspect of the picture’s relation to reality. Black (1964. or how he should not hold himself. Something like this view ﬁnds expression in Pitcher (1964) and Hallet (1977). the notion of an a priori analysis of the elementary propositions is held to be nonsensical. put together for the sake of experiment. that his Tractarian usage of the words darstellen and vorstellen is at this point ﬁrmly established. desire 153
4. 8.
5. 6. 57–8 of this study. 10. (“There cannot be a hierarchy of the forms of the elementary propositions. This declaration in fact also appears at the very start of the Notebooks. here mean “and. I am not suggesting.Notes to pp. Again. See pp. By “logical constant” I. Cf. See NB 2. See Anscombe (1959. 11. It is interesting to compare the above Notebooks passage to the passage in the Investigations. This will be how Frege thought of the ‘assumption’ ” (PI p. and so on. as we have seen.
. 10).
7. Hacker (1986) explicitly puts forward this interpretation: “The harmony between thought and reality seemed [to Wittgenstein in the Tractatus] forged by psychic structures (‘the language of thought’ as some cognitive psychologists today would have it).
9.) Central to understanding Wittgenstein’s point in presenting the general form of the proposition will then be to see how he abstracts away from the question of the inner constitution of the propositions he attempts to describe. also 4. expectation and its fulﬁllment. p. it became evident [to the later Wittgenstein]. but is maintained most explicitly and extensively in Hacker (1972). One might (using the language of chemistry) call this picture a proposition-radical. this notion is sufﬁciently distinct as to require separate treatment. or how a particular man did stand in such-andsuch a place. Just as in 1914. however. 76) explicitly asserts that vorstellen is used by Wittgenstein “interchangeably” with darstellen.521 makes clear.556).” and “ifthen.” There is then an important difference here from the situation as regards the elementary propositions. Wittgenstein would appear to understand this Fregean notion in accordance with his own idea of the presenting dimension of the picture. of course. See Goldfarb (unpublished) for an extremely clear and insightful criticism of these authors’ positions on this issue. should hold himself. 81–90
tion is between vorstellen and abbilden. pp.” Much of what Wittgenstein says about these also holds for the quantiﬁer. was confused on many counts. but. But this. Only that which we ourselves construct can we foresee” (TLP 5. As we have seen.” “not. which also deals with this notion: “Imagine a picture representing a boxer in a particular stance. 105–6 fn) for a discussion of this issue.” “or. Now this picture can be used to tell someone how he should stand.031: “In the proposition a state of affairs is. For.
12. belief and what makes it true.

comes largely to replace any early tendency toward the postulation of entities. They are like ideas in being nonspatial” (PW 148). Moore in Norway” refers to as the “Bedeutung” of the proposition. Emphasis on the use of the propositional/pictorial sign. 154
14. Bradley (1992.
20. One nice summary of his standard view is found in “Logic”: “Unlike ideas. 119). in the “Notes Dictated to G. also Frege’s denials of the possibility of illogical thought at BLA 12–13 and FA 20–1. the fact aRb.
15.g. thoughts do not belong to the individual mind (they are not subjective). This is an interesting way of putting it. one might say.
. I suggest that it is to avoid such a reiﬁcation that Wittgenstein soon gives up talk of a proposition’s Bedeutung. 35–47. 91–6
and its satisfaction make contact in grammar. the corresponding fact would be the fact aRb. This is what Wittgenstein means at 2. McDonough (1986. pp.. Black (1964. it encourages the very sort of (Russellian) reiﬁcation of facts that I claim Wittgenstein is attempting to undermine. 21. See Chapter I. 20. They are not the product of thinking. this is distinguished from the “sense2” of a proposition.” This likewise makes it appear that the sense of a proposition is what is represented when that proposition is true. describe these “twin aspects” taken together. See Russell’s claims in Philosophy of Logical Atomism. 90). p.2341: “Denial reverses the sense of a proposition. 119). especially since McDonough’s sense1 would seem to correspond to what Wittgenstein. which is a speciﬁcation of whether the existence of that which corresponds to the sense1 is to be “included” or “excluded” by the proposition. These internal relations are not bound together by a shadowy mental intermediary” (p. n. 151–2). who explicitly equates Wittgenstein’s position in the Tractatus with Russell’s in The Philosophy of Logical Atomism. McDonough’s formulation is potentially misleading. pp. in effect. pp. p. and confront each one of us in the same way (objectively). Cf. also the end of 5. 19.Notes to pp. (See NB 112: “The Bedeutung of a proposition is the fact that corresponds to it. and in the Tractatus expresses what he was previously reaching for now with the notion of a picture “presenting” states of affairs.22 when he says that a picture represents what it represents “through the pictorial form. but are independent of our thinking.”) Nonetheless. p. since by dividing up the notion of sense in this way.” if it’s true. for example. 17. Cf. In this regard they are like physical bodies. Such a claim is found in many passages in Frege’s writing.
22. E. 26–42) introduces the term “sense1” to.
18. Such a view is attributed to Wittgenstein by Bradley (1992. early on. 16. 23. but are only grasped by thinking.” See. 9). Hacker (1986. if our proposition be “aRb. What distinguishes them from physical bodies is that they are non-spatial and we could perhaps really go as far as to say that they are essentially timeless – at least inasmuch as they are immune from anything that could effect a change in their intrinsic nature. 70–78. if false. e.

p. Bradley (1992. “wise. but without some such measure. in the end. 25. 26. after we had stumbled upon a proof of it” (p. as Dreben and Floyd (1991. he could never admit that the tautological character of a proposition might reveal itself by accident. Fogelin (1996. nearly always take the form of sentences “which obey ordinary rules of grammar” she remarks: “Wittgenstein is questioning the idea that ordinary grammar is adequate to guarantee sense” (p. 318–19). assume such an interpretation of the Tractatus. 194–5) for an elaboration of this idea. 30. Although. 2000. of course.Notes to pp. 27. Noting that what the Tractatus identiﬁes as the unsinnig pseudo-propositions of philosophy. p. pp. 32. pp. 6–7. 244–50. even if this acceptance comes with “grumbles from the side of the picture theory” expressed as 4.” 28. simply means that the propositional constituent is here being used in a manner that is not consonant with its ordinary logicosyntactical employment.” in this context and hence give the word a meaning. 84). See again Dreben and Floyd (1991) for an excellent discussion of this whole issue. seeing a tension in Wittgenstein’s views. 17–20) goes so far as to attribute this interpretation of “tautology” to Wittgenstein himself.466’s reference to these as “the disintegration of the combination of signs. pp. 95–114) and Conant (1991. 82) and Black (1964. That is. 33. 98–103
24. Black (1964. maintains that he does not in fact ultimately deny the status of propositionhood to the strings of logic.4733). Juliet Floyd (1998) puts the general point well. NB 109: “This is the actual procedure of [the] old Logic: it gives 155
. legitimate combinations of signs. Black maintains: “The need for known decision procedures for checking on putative logical truths is an integral and indispensable feature of Wittgenstein’s philosophy of logic. Thus Wittgenstein says that the sentence “Socrates is identical” makes no sense not because we have produced an illogical thought – we cannot go wrong at the level of the expression since. pp. as it were. 1998. as well as the sinnlos tautologies and contradictions. 31. among others. p. Wittgenstein does indeed originally believe that his “ab-notation” can be extended to all of logic and appears to arrive at his characterization of logical propositions as tautologies with that in mind. pp. Fogelin (1996. 341–2. See Diamond (1991. That. For he would ﬁnd it intolerable that we might understand a proposition without knowing in advance how to ﬁnd out whether it was a tautology or contradiction. 319). See CL 60–1. 29. the expression is nothing but the sign in its signiﬁcant use – but because “we have given no meaning to the word ‘identical’ as adjective” (TLP 5. Thus. say. we must recognize we have not as yet constructed a genuine proposition. as we have seen. 32) point out. See pp. It is open to us to map the use of “identical” to that of. pp. his “theory of truth-functionality” forces him to grant that tautologies and contradictions are. pp. Cf. 319). 46–7).

42.
37.Notes to pp. it tells you something about the kind of proposition you have got. 36.” Brockhaus (1991.
44. 64–7. there is a class of propositions which are all the values of the resulting variable proposition.
38. p. 216) suggest a connection between the Carroll article and the Tractatus’ view of inference rules.
43. and then says that what you get by applying the rules to the propositions is a logical proposition that you have proved. to a logical prototype (einem logischen Urbild).” Mounce (1981. 109). p. 198). p. 41) also makes this point.” This point was earlier made on p. See Lewis Carroll (1895).126] – the emphasis. p. 104–13
so-called primitive propositions.” See. 41. for example. But this is now no longer dependent on any agreement.” The possibility of this sort of logical ascent with regard to the variable would appear to have been already introduced at 3. See again Black (1964. for example. Moore in Norway” Wittgenstein in fact immediately follows his account of logical propositions as “forms of proof” with a discussion of the theory of types (NB. But if we change all those signs. we can identify tautologies through purely formal rules for manipulating signs. 338) comments: “In view of what follows immediately. where Wittgenstein makes reference to a “nonarbitrarily determined” class of propositions: “If we change a constituent part of a proposition into a variable.334 and our discussion on pp. Note that in “Notes Dictated to G. so-called rules of deduction. is Wittgenstein’s – implies that insofar as the sense of elementary propositions is guaranteed. even while acknowledging Wittgenstein’s intentional use of the former term: “The occurrence of ‘symbol’ in the ﬁrst remark and ‘sign’ in the second [the second sentence of 6. 338).331–3. In more linguistic terms. by arbitrary agreement. Both Ricketts (1996. 35. E. Cf. into variables. this is just to say that the application of the logical constants will never take us beyond the domain of the (signiﬁcant) proposition. 5. one might have expected to ﬁnd ‘sign’ instead. whose meaning was arbitrarily determined. p. p. 39. 204) seems to ignore the difference between symbol and sign. See also TLP 3. it depends only on the nature of the proposition.315. Black (1964.
156
. there always remains such a class. by the way. 216) and Glock (1996.47:
34. A number of commentators have wondered at the appearance of the term “symbol” at this point. This class in general depends on what.
40. Thus. Cahoone (1995. for we can recognize in an adequate notation the formal properties of the propositions by mere inspection. The truth is. p.122 “Whence it follows that we can get on without logical propositions. 72. viz that it can be derived from the ﬁrst symbols by these rules of combination ( is a tautology). It corresponds to a logical form. 6. we mean by parts of that proposition. Cf.

Nonetheless. all logical constants already are. One way to understand the middle and later Wittgenstein’s shift away from the perspective of the Tractatus is to see him as giving up precisely this sharp distinction between general form and logical form. the rules for the logical constants form only a part of a more comprehensive syntax about which I did not yet know anything at that time” (VC 74).
47. Fogelin acknowledges that “it is hard to read this passage without feeling let down. Wittgenstein is not. in January 1930. Cf. to be at one place in the visual ﬁeld is impossible.x a. 47–9). Here no logical product can be constructed. et al. also Wittgenstein’s claim at the end of the Preface: “And if I am not mistaken in this. For all logical operations are already contained in the elementary proposition. 48). for example. For “fa” says the same as “(∃x). of course.” Of course. suggesting that in the Tractatus he believed that one could say that red and blue are at one point simultaneously – this impossibility is explicitly afﬁrmed at 6. and did not think that these rules might have something to do with the inner structure of propositions.
48. I cannot.” but perhaps more clearly in some of his conversations with Schlick. in the late 1920s and early 1930s. Rather.q’. Waismann. Thus. That is not how things actually are. it may even seem a joke” (p.g. for example ‘p.3751: “For two colours. Indeed. “given the elaborate wind-up.
46. 114–15
It is clear that everything which can be said beforehand about the form of all propositions at all can be said on one occasion. say that red and blue are at one point simultaneously. See Fogelin (1996. there is argument and function. for example. he maintains that Wittgenstein is “dead serious. Wittgenstein describes his earlier conception in this way: “I laid down rules for the syntactical use of logical constants. and where these are. then the value of this work secondly consists in the fact that it shows how little has been done when [the problems of philosophy] have been solved” (TLP Preface). pp. I do not deny that Wittgenstein is here serious – it is a question of what is the import of that seriousness. That however is the general form of proposition.” Where there is composition. I owe this way of putting the matter to Juliet Floyd. indeed. have in common with one another.Notes to pp. much of this section has been inspired by her work (unpublished) on the general form of the proposition.” that.
157
. according to their nature.
45. between what can be characterized in advance and what is intrinsic to the particular picture/proposition as such. Wittgenstein’s dissatisfaction with the Tractatus view expresses itself initially in the so-called Color Exclusion Problem discussed in “Some Remarks on Logical Form. e.fx. What was wrong about my conception was that I believed that the syntax of logical constants could be laid down without paying attention to the inner connection of propositions. One could say: the one logical constant is that which all propositions.

Frascolla (1994.Notes to pp.” Rather. the incorrect multiplicity.. It is also all too obvious that this theory isn’t what is in question either in the Grundgesetze. As he puts it in his conversations with the Vienna positivists: “At that time [the time of the Tractatus] I thought that all inference was based on tautological form. 8) misconstrues 5. p. Thus he begins to focus on how the notion of logical inference is applicable in the case of sentences that would seem to share a logical form. of the Tractatus’ speciﬁcation of the general propositional form. this is just to suggest that. etc. however. Glock (1996. Pears (1987. rather. 110–13.g. 214–18). 147–8). pp. in contrast with what the Tractatus claims. he is simply ignoring Wittgenstein’s special use of the term “function. and Stern (1995. then the whole theory of things. Stenius (1960. 200).
52. pp. the inner structure of the proposition. it forces a shift in Wittgenstein’s conception of those unsinnig pseudo-statements – or. That insight marks the transistion to the far less structured. If syntactical rules for functions can be set up at all (ueberhaupt). 65–6.” Even Hylton’s much more careful discussion of this 158
49. in his conception of how one should elucidate their Unsinnigkeit. Once more: logic must take care of itself” (NB 2). Hacker (1986. of course. the opening of the Notebooks: “Logic must take care of itself. for example. properties.” While the Tractatus does. so to speak. since he says that what is said about operations can just as well be said of a function like “x2. In coming to recognize that no analysis of color propositions into logically independent elementary propositions is forthcoming.
50. is describable in terms of rules – that we can to a certain extent offer a grammar of logico-pictorial form. At that time I had not yet seen that an inference can also have the form: This man is 2m tall. the point is that he had thought this impossibility to be expressible in terms of the logic capturable by his N operator and thus to require the nonelementary nature of propositions ascribing color. multifarious approach that characterizes Wittgenstein’s work for the rest of his life. 22–3). The parallels between the Tractatus and Kant’s First Critique have been often noted. Cf. for it is excluded by the logical structure of colour. Wittgenstein is acknowledging the similarity of color exclusion statements (e. deny the existence of logical objects. especially chapter I). that is not what is at issue here. 258) disputes Wittgenstein’s claim here. 132. or in Principia Mathematica. See. incompatible with the logico-pictorial forms. therefore he is not 3m tall” (VC 64). At the same time.
51. After all. is superﬂuous.25 as suggesting (in part) that “there is no object that corresponds to an operation sign as its ﬁxed and distinguishable semantic value. Brockhaus (1991. This then brings out the inadequacy. “Point A is red at time T and point A is blue at time T”) taken as they stand to nonsensical statements – the pseudo-statements (such as “Socrates is identical”) that are. pp. p. its pictorial character. For Wittgenstein. to “characterize the sense of a proposition” is not to point to some thing – for then propositions would be understood as names. p. 116–17
logically impossible. especially chapter II). Black (1964.
.” Here.

Notes to p. 119
issue in “Functions, Operations, and Sense in Wittgenstein’s Tractatus’’ (1997) does not, I suggest, pay sufﬁcient attention to the internal logic of the Tractatus, tying Wittgenstein’s perspective too closely to that of Frege and Russell. Juliet Floyd (unpublished) has forcefully stressed this point. See also Wittgenstein’s reﬂections in the Notebooks: “If a sentence were ever going to be constructable it would already be constructable. We now need a clariﬁcation of the concept of the atomic function and the concept ‘and so on.’ The concept ‘and so on’ symbolized by ‘ . . . ’ is one of the most important of all and like all the others inﬁnitely fundamental. For it alone justiﬁes us in constructing logic and mathematics ‘so on’ from the fundamental laws and primitive signs. The ‘and so on’ makes its appearance right away at the very beginning of the old logic [the logic of Frege and Russell] when it is said that after the primitive signs have been given we can develop one sign after another ‘so on.’ Without this concept we should be stuck at the primitive signs and could not go ‘on’ ”(NB 89–90). Note that this occurrence of the ellipsis is not an instance of what Wittgenstein is here talking about (in Tractarian terms, it signiﬁes a different symbol). Rather, it constitutes an analogue to a schema for a logical form. In light of this point and what was said just above in note 48 about Wittgenstein’s development, one might suppose that his later thought involves showing, in effect, how there is an account to be given of why a noise cannot have a weight. But that is not quite accurate; Wittgenstein’s later thought is not simply a matter of showing how the Tractarian analysis of the general form of the proposition can be extended to the forms of the elementary propositions. Instead, the rejection of the sharp distinction between general and logico-pictorial form cuts both ways. That is, just as the notion of logical inference is brought to bear in the context of the inner (or, as Wittgenstein might earlier have said, “pictorial”) makeup of the proposition, so what we might call the “groundlessness” that characterizes the latter is seen as also applying to the former. Hence, we ﬁnd the later Wittgenstein in his discussions of rule following fundamentally questioning the “determinacy” that seems to belong to logic. Note here how we are called back to the opening remarks of the Tractatus and the association of logic with possibility. As always, Wittgenstein will not deny his own seemingly robustly metaphysical claims – he does not assert “p” only later to surreptitiously withdraw it – but, rather, seeks just to make manifest what, in the end, these claims come to. Actually, there is, as Fogelin (1976, pp. 78–82) has pointed out, a difﬁculty in generating certain multiply quantiﬁed formulas – for example, the formula “∀x∃yFxy” – using Wittgenstein’s notation, since we are not given any way of making scope distinctions. Fogelin takes this to indicate a “fundamental error” in the logic of the Tractatus. It is easy enough, however, to amend the Tractarian notation so as to make it expressively complete, as Geach (1981, pp. 168–71; 1982, pp. 127–8), Soames (1983, 159

53. 54.

55.

56.

57.

58.

Notes to pp. 119–23
573–89), and Floyd (unpublished) have shown. And since, as Soames also points out, Wittgenstein himself at 4.0411 notes the importance of a notation’s ability to express distinctions of scope, it seems overly pedantic to ﬁnd serious fault with the Tractatus for the absence of any explicit instructions on this score. At 5.523, Wittgenstein in fact would appear to suggest that our whole understanding of generality turns around this initial speciﬁcation: “The generality symbol occurs as an argument” (TLP 5.523). The point, in other words, is that generality is already contained in the “x” in a propositional variable like “x is a table” – the quantiﬁer does not somehow itself manage to confer this property. It is to make this evident that Wittgenstein’s notation dispenses altogether with a sign for the quantiﬁer. Mounce (1981, pp. 65–72) argues for this view. See especially Principia Mathematica, pp. 38–41. Cf. this Notebooks assertion from 1915: “All APPEARS to be nearer the content of the proposition than to the form. . . . Generality is essentially connected with the elementary FORM. The liberating word – ?” (NB 39; caps Wittgenstein’s). It is important for our understanding of Wittgenstein’s development to here reiterate the point made last chapter (see note 17, chapter II) about how he comes to see himself as confused on this issue. For while the Tractatus’ emphasis on the ellipsis is meant to bring out the unclarity of the notion of an inﬁnite disjunction, the idea of a complete analysis seems ultimately to rest on this conception. After all, the possibility of completing the analysis of this occurrence of “on the table” can only be realized if, in the end, we can make a comprehensive list of spatial locations. In the Tractatus, then, the dots in the above formal series must be understood as marking only some sort of present limitation on our analytical capacities, whereas the later Wittgenstein brings out much more sharply how, for him, it makes no sense to imagine such a possibility. Or more properly, “schema for a variable,” since serves only as a placeholder for some particular propositional variable. Note how the use of the term vertreten here mirrors its use at 2.31 and 3.22, where, we recall, it served to describe how the pictorial/propositional constituents “stand in” (or “go proxy”) for their counterparts in the world. Here I am again indebted to Juliet Floyd (unpublished), who develops this idea in an original and very illuminating discussion of the Tractatus’ treatment of “number.” Cf. Wittgenstein’s 1919 letter to Russell: “I suppose you didn’t understand the way, how I separate in the old notation of generality what is in it truth-function and what is purely generality. A general prop[osition] is A truth-function of all PROP[OSITION]S of a certain form” (NB 131); caps Wittgenstein’s). Wittgenstein also acknowledges this in the same 1919 letter to Russell

59.

60. 61. 62.

63.

64. 65.

66.

67.

68.

160

Notes to pp. 123–31
referred to in the previous note: “You are quite right in saying ‘N( )’ may also be made to mean p v q v r v. . . . But this doesn’t matter!” (NB 131). 69. See Fogelin (1976, p. 80): “The expression “(x:N(fx))” [Geach’s way of expressing one application of N to a function “fx”] speciﬁes (or is shorthand for) a set of propositions that is the result of possibly inﬁnitely many (unordered) applications of the operator N to a possibly inﬁnite set of propositions.” Fogelin then goes on to argue that this requirement is inconsistent with 5.32’s assertion that all such applications must be ﬁnite. As he puts it: “If the set of base propositions is inﬁnite, then nothing will count as the immediate predecessor of the ﬁnal application of the operation N in the construction of a universally quantiﬁed proposition” (p. 81). Chapter IV 1. For accuracy, we would have to add here “in a certain respect.” For the fundamental distinction we have emphasized between the general form of the proposition and the (anumerical) logical forms entails that no systematic presentation can be given of the inner structure of the proposition, its internal relation to the world. 2. Besides, Wittgenstein’s later thought is not in a fundamentally different position with respect to the particular problem we are here addressing: we still may wonder about how that work is to be applied to philosophical confusions that it does not speciﬁcally treat. 3. Cf. PO 165: “Indeed we can only convict someone else of a mistake if he acknowledges that this really is the expression of his feeling. For only if he acknowledges it as such, is it the correct expression. (Psychoanalysis). What the other person acknowledges is the analogy I am proposing to him as the source of his thought.” 4. Cf. CV 16: “Working in philosophy – like work in architecture in many respects – is really more a working on oneself. On one’s own interpretation. On one’s way of seeing things. (And what one expects of them).” 5. Conant (1998; pp. 247–8) makes a similar point. 6. In a similar vein, Rhees (1998, p. 40) asserts: “And that is what has to be pressed against those who think of philosophy as therapeutic. Something we have to indulge in because some people are unfortunate. You could never understand why Wittgenstein (and others) have wanted to compare philosophy with poems, in that case. The man who ﬁnds life difﬁcult. And the man who wants to ‘put the difﬁculties right’.” 7. One cannot but think here of Russell’s ongoing worry about the need for immediate contact between the mind and reality, as it is expressed in his early rejection of idealism, in his notion of knowledge by acquaintance, and so forth. For Wittgenstein, Russell’s attempts to “secure” this connection through some kind of elaborate account are paradigmatic of

161

Note also that in both the Tractatus and the Notebooks the quoted phrase is prefaced by the words “We feel that”. but at the same time emphasizing that it is no more than a sense. but just in the recognition that “there are no questions any more.
. that he cannot simply be described in general as “pro” or “con. Wittgenstein is describing the sense that gives rise to philosophical perplexity. “philosophy” (which Wittgenstein is seen as wanting in some sense to counter) for “the mystical” in that passage. p. it would then be mistaken to substitute. draw a limit to thinking. than to follow Aristotle’s ideal and to do good spontaneously out of habit. in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able 162
8. a feeling. the tendency amongst commentators (Russell included) has been to understand the early Wittgenstein as in fact endorsing some version of mysticism. the reader is not thereby committed to attributing to Wittgenstein the view that “everything” must be stateable (whatever that would mean) – still less to supposing that the notion of an ineffable content is Wittgenstein’s real target in the Tractatus. Shields (1993. as fundamentally rejecting any notion of mysticism. 131–2
philosophical confusion. but to the expression of thoughts. Note that the identical phrase appears at 6. therefore.52 of the Tractatus. While it may certainly be granted that the text’s notion of showing does not involve a gesture toward an ineffable truth (and that one way of understanding the mystic would be to attribute to him the desire to make such a gesture). One gets the impression that it is somehow better to undergo a prolonged spiritual struggle in the pursuit of righteousness. it seems quite clear that in this context anyway he is decidedly not embracing a mystical stance. as Conant (see especially 1991) and Diamond sometimes imply.” For if we look at the whole of the remark from Notebooks 51.
10. The response he ultimately points to does not lie in a wordless ﬂood of insight. But I would urge that Wittgenstein’s attitude toward mysticism is not univocal.
9. for.
11. By contrast. than for those who were never bothered at all. We might say that the essential thrust of the Tractatus is to get us to see that such a connection can only be shown.” Recall Wittgenstein’s claim in the Preface: “The book will. On this reading. 63) makes a similar observation: “[Wittgenstein] seems to have more respect for someone who is seriously enmeshed and bothered by metaphysical difﬁculties. I believe that we misconstrue the Tractatus’ overall aims when we see Wittgenstein.Notes to pp.” That familiar-sounding “solution” would suggest that the mystical urge is seen as here appearing in very philosophical guise. although in an apparently different context (see the following footnote). at least in the sense of imagining an ineffable “answer” to all outstanding nonscientiﬁc questions. as I do.” Given the standard interpretation of the Tractarian notion of showing as resting on the possibility of an ineffable content. or rather – not to thinking. It should be noted that this Notebooks passage occurs in the context of Wittgenstein’s discussion of what he calls “the urge towards the mystical. however.

It implies that there is some special state or experience that philosophers are somehow blinded to. of course. is not to deny that another might point out to me the apparent peculiarity of my utterances.641). Compare this also with the similar idea that we saw expressed in connection with the discussion of analysis. pp. he can see that he is wrong just by recalling that there was a time when this ‘solution’ had not been discovered.
13. why this notion is particularly prominent in the closing pages of the book (see especially TLP 5. see. In this vein. but rather abandon a certain combination of words as senseless. philosophy does not lead me to any renunciation. And it is the same in the study of logic. in a certain sense.. And maybe that is what makes it so difﬁcult for many.g. also this remark from the “Big Typescript”: “As I have often said. BUT THE DIFFICULTY OF A CHANGE 163
12. vii ff. just as it is difﬁcult to hold back tears. 132–3
to think what cannot be thought). for Wittgenstein only I can recognize my propositions as nonsense.
. or an outburst of anger” (PO 161). One might then say that. One is also reminded here of this remark from Culture and Value: “If anyone should think he has solved the problem of life and feel like telling himself that everything is quite easy now. 212 ff. Wittgenstein will not allow us to say that he is returning us to anything in particular. it is sometimes suggested that Wittgenstein’s aim is therefore to return us to “the ordinary”. however. But this is misleading.
15. Cf.62–5. The limit can. since I do not abstain from saying something. philosophy requires a resignation. If there were a ‘solution’ to the problems of logic (philosophy) we should only need to caution ourselves that there was a time when they had not been solved (and even at that time people must have known how to live and think)” (CV 4).Notes to pp. is nonsense. this emphatic declaration at the beginning of section 86 of the “Big Typescript”: “DIFFICULTY OF PHILOSOPHY NOT THE INTELLECTUAL DIFFICULTY OF THE SCIENCES. The possibility of expressing matters in this way can help us to see the importance of solipsism for Wittgenstein.
14. but it must have been possible to live then too and the solution which has now been discovered seems fortuitous in relation to how things were then. for Wittgenstein. Cf. but I alone can call them nonsense. There is simply the process of being freed from philosophical illusions. Putnam’s (1993. To posit a general notion of “ordinary experience” is to engage in just the sort of a priori categorization that the Tractatus. seeks to explode. That.) account of what he calls the “ ‘end of philosophy’ reading of Wittgenstein”. but one of feeling and not of intellect. therefore. as we have seen. e. Despite the philosopher’s yearning to see his enterprise – even in its disappearance – as aiming toward some deﬁnite end. In another sense. only be drawn in language and what lies on the other side of the limit will be simply nonsense” (TLP p. the claim that “I know what I mean” by the vague proposition (see NB 70 and pp. 27). of this study). It can be difﬁcult not to use an expression. This.

caps Wittgenstein’s).
164
. RESISTANCES OF THE WILL (des willens) MUST BE OVERCOME” (PO 161. but rather an internal feature of his way of relating to the world. Still. Thus. For this reason then the Tractatus speaks of the ethical world as “wax[ing] and wan[ing] as a whole” (TLP 6. 16.43 calls the “world of the happy” – is characterized just by complete agreement between the self and its world. Of course.Notes to pp. that it is a reluctance to acknowledge the world as independent of my will. Or one could say. 17. for Wittgenstein such harmony is not a genuine property of an individual’s life. By contrast.373. 133–4
OF ATTITUDE. in the language of 6. one element that might be present or absent. the state to which the Tractatus aims to bring us – what Wittgenstein at 6.43). 18. the Notebooks remarks: “The happy life seems to be in some sense more harmonious than the unhappy” (NB 78). we note that in PI 133 the original demand for “complete clarity” and the complete disappearance of philosophical problems remains.